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------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADywAAAAUAIgAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC1P8A AAAAAACQAQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACIgAAADIKMABHARIAAABFcXVhdGlvbnMgb2YgTGluZXMd ABkAGQAYAAwACwAYABgAFwAMABgADQANABgACgAZABgAFgAEAAAALgEAABwAAAD7AhAABwAAAAAA vAIAAAAAAQICIlN5c3RlbQAAAAAAABgAAAAsnhMAAQAAAOQEAAAAAAAABAAAAC0BBAAEAAAA8AED AAMAAAAAAA== ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0060.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0104.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
We have two points on the line (1, –2), (–4, 0) and we
need the slope.
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0105.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Δy
Δx
We have two points on the line (1, –2), (–4, 0) and we
need the slope. By the slope formula,   
m
=3D
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0105_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0106.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Δy
Δx
0 – (–= ;2 )
–4 – (1)
=3D
We have two points on the line (1, –2), (–4, 0) and we
need the slope. By the slope formula,   
m
=3D
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0106_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0106_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABH AAIAgAAAAAAzAAIKjI+py+0Po5xUFQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0107.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Δy
Δx
0 – (–= ;2 )
–4 – (1)
2
–5
=3D
We have two points on the line (1, –2), (–4, 0) and we
need the slope. By the slope formula,   
=3D
m
=3D
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0107_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0107_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABH AAIAgAAAAAAzAAIKjI+py+0Po5xUFQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0107_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0108.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Δy
Δx
0 – (–= ;2 )
–4 – (1)
2
–5
=3D
We have two points on the line (1, –2), (–4, 0) and we
need the slope. By the slope formula,   
=3D
Hence, u= sing the point (–4, 0),
m
=3D
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0108_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0108_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABH AAIAgAAAAAAzAAIKjI+py+0Po5xUFQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0108_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0109.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Δy
Δx
0 – (–= ;2 )
–4 – (1)
2
–5
=3D
y =3D
We have two points on the line (1, –2), (–4, 0) and we
need the slope. By the slope formula,   
=3D
Hence, u= sing the point (–4, 0), the equation is
5
–2
(x – (–4)) + 0
m
=3D
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0109_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0109_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABH AAIAgAAAAAAzAAIKjI+py+0Po5xUFQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0109_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0109_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0110.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Δy
Δx
0 – (–= ;2 )
–4 – (1)
2
–5
=3D
y =3D
We have two points on the line (1, –2), (–4, 0) and we
need the slope. By the slope formula,   
=3D
Hence, u= sing the point (–4, 0), the equation is
5
–2
(x – (–4)) + 0
m
=3D
y =3D
(x + 4)
5
–2
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0110_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0110_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABH AAIAgAAAAAAzAAIKjI+py+0Po5xUFQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0110_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0110_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0110_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0111.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Δy
Δx
0 – (–= ;2 )
–4 – (1)
2
–5
=3D
y =3D
We have two points on the line (1, –2), (–4, 0) and we
need the slope. By the slope formula,   
=3D
Hence, u= sing the point (–4, 0), the equation is
5
–2
(x – (–4)) + 0
m
=3D
y =3D
(x + 4)
5
–2
y =3D
x –
5
–2
8
5
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0111_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0111_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABH AAIAgAAAAAAzAAIKjI+py+0Po5xUFQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0111_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0111_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0111_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0111_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAEAgAAAAAAzAAIEjI+pWQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0111_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAV AAEAgAAAAAAzAAIEjI+pBQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0112.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
b. The line that contains (1, –2) with the x-intercept at –4.
Δy
Δx
0 – (–= ;2 )
–4 – (1)
2
–5
=3D
y =3D
We have two points on the line (1, –2), (–4, 0) and we
need the slope. By the slope formula,   
=3D
Hence, u= sing the point (–4, 0), the equation is
5
–2
(x – (–4)) + 0
m
=3D
y =3D
(x + 4)
5
–2
y =3D
x –
5
–2
8
5
Equations of Lin= es
Recall th= at parallel lines have the same slope and perpendicular lines ha= ve slopes that are the negative reciprocal of each oth= er.
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0112_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0112_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABH AAIAgAAAAAAzAAIKjI+py+0Po5xUFQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0112_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0112_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0112_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0112_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAEAgAAAAAAzAAIEjI+pWQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0112_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAV AAEAgAAAAAAzAAIEjI+pBQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0062.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
Equations of Lin= es
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c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0114.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
To find = the slope of 3y – 4x =3D 2, solve for the y.
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c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
To find = the slope of 3y – 4x =3D 2, solve for the y.
3y =3D 4= x + 2
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c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
To find = the slope of 3y – 4x =3D 2, solve for the y.
3y =3D 4= x + 2
y =3D
4
3
x + 
2
3
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0116_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0116_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAzAAIEjI+pVgA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0117.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
4
3
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
To find = the slope of 3y – 4x =3D 2, solve for the y.
Therefor= e the slope of the line 3y – 4x =3D 2 is       .
3y =3D 4= x + 2
y =3D
4
3
x + 
2
3
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0117_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0117_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0117_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAzAAIEjI+pVgA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0118.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
4
3
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
To find = the slope of 3y – 4x =3D 2, solve for the y.
Therefor= e the slope of the line 3y – 4x =3D 2 is       .
3y =3D 4= x + 2
y =3D
4
3
x + 
2
3
So our l= ine has slope     &n= bsp; .
4
3
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0118_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0118_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0118_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAzAAIEjI+pVgA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0118_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAZ AAIAgAAAAAAzAAIGjI+py50FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0119.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
4
3
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
To find = the slope of 3y – 4x =3D 2, solve for the y.
Therefor= e the slope of the line 3y – 4x =3D 2 is       .
3y =3D 4= x + 2
y =3D
4
3
x + 
2
3
By the point-slope formula, the equation is  
So our l= ine has slope     &n= bsp; .
4
3
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0119_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0119_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0119_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAzAAIEjI+pVgA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0119_image045.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAZ AAIAgAAAAAAzAAIGjI+py50FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0120.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
4
3
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
To find = the slope of 3y – 4x =3D 2, solve for the y.
Therefor= e the slope of the line 3y – 4x =3D 2 is       .
3y =3D 4= x + 2
y =3D
4
3
x + 
2
3
y =3D      (x –= ; 3) + (–1)
By the point-slope formula, the equation is  
So our l= ine has slope     &n= bsp; .
4
3
4
3
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0120_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0120_image047.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0120_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAzAAIEjI+pVgA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0120_image049.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAZ AAIAgAAAAAAzAAIGjI+py50FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0120_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAAAzAAIEjI95BQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0121.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
c. The line that passes through (3, –1) and is parallel to th= e line 3y – 4x =3D 2.
4
3
Equations of Lin= es
Our line= have the same slope as the line 3y – 4x =3D 2.
To find = the slope of 3y – 4x =3D 2, solve for the y.
Therefor= e the slope of the line 3y – 4x =3D 2 is       .
3y =3D 4= x + 2
y =3D
4
3
x + 
2
3
y =3D      (x –= ; 3) + (–1)
By the point-slope formula, the equation is  
So our l= ine has slope     &n= bsp; .
4
3
4
3
y =3D
4
3
x=
– 4 – 1
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0121_image051.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0121_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0121_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAAAzAAIEjI+pVgA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0121_image054.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAZ AAIAgAAAAAAzAAIGjI+py50FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0121_image055.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAAAzAAIEjI95BQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0121_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAIAgAAAAAAzAAIFjI+pywUAOw== ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0048.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
d. The line that with y-intercept –3 and is perpendicular to = the line 2x – 3y =3D 2.
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0122.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
d. The line that with y-intercept –3 and is perpendicular to = the line 2x – 3y =3D 2.
Equations of Lin= es
For the slope, solve 2x – 3y =3D 2
        = ;            &n= bsp;            = ;    
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0123.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
d. The line that with y-intercept –3 and is perpendicular to = the line 2x – 3y =3D 2.
Equations of Lin= es
For the slope, solve 2x – 3y =3D 2
        = ;            &n= bsp;            = ;     –3y =3D –2x + 2=
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0124.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
d. The line that with y-intercept –3 and is perpendicular to = the line 2x – 3y =3D 2.
2
3
Equations of Lin= es
For the slope, solve 2x – 3y =3D 2
        = ;            &n= bsp;            = ;     –3y =3D –2x + 2
        = ;            &n= bsp;            = ;         y =3D
2
3
x
–
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0124_image057.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0124_image058.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0125.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
d. The line that with y-intercept –3 and is perpendicular to = the line 2x – 3y =3D 2.
2
3
Equations of Lin= es
For the slope, solve 2x – 3y =3D 2
        = ;            &n= bsp;            = ;     –3y =3D –2x + 2
        = ;            &n= bsp;            = ;         y =3D
2
3
x
–
Hence the slope of 2x – 3y =3D 2 is        .
2
3
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0125_image059.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0125_image060.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0125_image061.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0126.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
d. The line that with y-intercept –3 and is perpendicular to = the line 2x – 3y =3D 2.
2
3
Equations of Lin= es
For the slope, solve 2x – 3y =3D 2
        = ;            &n= bsp;            = ;     –3y =3D –2x + 2
        = ;            &n= bsp;            = ;         y =3D
Since perpendicular lines have slopes that are the
negative reciprocal of each other, our slope is       .   
2
3
x
–
Hence the slope of 2x – 3y =3D 2 is        .
2
3
–3
2
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0126_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0126_image063.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0126_image064.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0126_image065.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0127.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
d. The line that with y-intercept –3 and is perpendicular to = the line 2x – 3y =3D 2.
2
3
Equations of Lin= es
For the slope, solve 2x – 3y =3D 2
        = ;            &n= bsp;            = ;     –3y =3D –2x + 2
        = ;            &n= bsp;            = ;         y =3D
2
3
x
–
Hence the slope of 2x – 3y =3D 2 is        .
2
3
Hence the equation for our line is
y =3D       (x – (0)) + (–3)
–3
2
Since perpendicular lines have slopes that are the
negative reciprocal of each other, our slope is       .   
–3
2
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0127_image066.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0127_image067.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0127_image068.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0127_image069.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAEAgAAAAAAzAAIEjI+pWQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0127_image070.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0128.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
d. The line that with y-intercept –3 and is perpendicular to = the line 2x – 3y =3D 2.
2
3
Equations of Lin= es
For the slope, solve 2x – 3y =3D 2
        = ;            &n= bsp;            = ;     –3y =3D –2x + 2
        = ;            &n= bsp;            = ;         y =3D
2
3
x
–
Hence the slope of 2x – 3y =3D 2 is        .
2
3
Hence the equation for our line is
y =3D       (x – (0)) + (–3)
–3
2
y =3D       x &= #8211; 3  
–3
2
Since perpendicular lines have slopes that are the
negative reciprocal of each other, our slope is       .   
–3
2
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0128_image071.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0128_image072.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0128_image073.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0128_image074.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAEAgAAAAAAzAAIEjI+pWQA7 ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0128_image075.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0128_image076.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAa AAIAgAAAAAAzAAIGjI+py70FADs= ------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0057.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
Example:=   The price of a lap top computer is dropping.  In the year 2000, the most inexpensive laptop cost $900, in the year 2005, the most inexpensive one cost $500.  Assume the price is linea= r, find the equation of the price in terms of time.
What is = the projected price in the year 2009?
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0129.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
Example:=   The price of a lap top computer is dropping.  In the year 2000, the most inexpensive laptop cost $900, in the year 2005, the most inexpensive one cost $500.  Assume the price is linea= r, find the equation of the price in terms of time.
What is = the projected price in the year 2009?
Let the = year 2000 be the year x =3D 0,
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0130.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
Example:=   The price of a lap top computer is dropping.  In the year 2000, the most inexpensive laptop cost $900, in the year 2005, the most inexpensive one cost $500.  Assume the price is linea= r, find the equation of the price in terms of time.
What is = the projected price in the year 2009?
Let the = year 2000 be the year x =3D 0, so the year 2005 is x =3D 5.
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0131.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
Example:=   The price of a lap top computer is dropping.  In the year 2000, the most inexpensive laptop cost $900, in the year 2005, the most inexpensive one cost $500.  Assume the price is linea= r, find the equation of the price in terms of time.
What is = the projected price in the year 2009?
Let the = year 2000 be the year x =3D 0, so the year 2005 is x =3D 5. Let y =3D price of a laptop. 
Equations of Lin= es
------=_NextPart_01C9656C.E4F00BA0 Content-Location: file:///C:/CEF64513/3EquationsofLines_files/slide0132.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Equations of Lines
Example:=   The price of a lap top computer is dropping.  In the