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7/30/2019 Obj. 3 Equations of Lines
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Obj. 3 Equations of Lines
The student will be able to (I can)
Use slopes and equations of lines to investigategeometric
relationships
Use equations of lines to solve problems.
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7/30/2019 Obj. 3 Equations of Lines
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Point-Slope
Form
Given the slope, mmmm, and a point on the line
(xxxx1111,yyyy1111), the equation of the line is
y yyyy1111 = mmmm(x xxxx1111)
Example: Write the equation of the linewhose slope is 2222,
which goes through thepoint (1111, 6666)
y 6666 = 2222(x 1111)
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7/30/2019 Obj. 3 Equations of Lines
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Slope-
Intercept Form
Given the slope, mmmm, and bbbb, the y-intercept,
the equation of the line is
y = mmmmx + bbbb
Example: For mmmm = 3333 and y-intercept 7777,find the equation
of the line.
y = 3333x + 7777
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7/30/2019 Obj. 3 Equations of Lines
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Horizontal Line
Vertical Line
For a horizontal line (mmmm = 0000), the equation
of the line is
y = bbbb
For a vertical line (mmmm =
undefinedundefinedundefinedundefined), theequation of the line
is
x = xxxx1111
Notice that this equation does not startwith y=
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7/30/2019 Obj. 3 Equations of Lines
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PracticeWrite the equations in point-slope form
1. m = 2; (3, 5) 2. (1, 2)
y 5 = 2(x 3)
3. m = 4; (1, 4) 4. (2, 3)y 4= 4(x + 1)
Write the equations in slope-intercept form5. m = 6, b = 2 6. m
= 1, b = 4
y = 6x + 2 y = x 4
2m ;
3=
3
m ;4=
2y 2 (x 1)
3 =
3y 3 (x 2)
4+ = +
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7/30/2019 Obj. 3 Equations of Lines
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Practice7. Write the equation of the line through (1111, 0000)
and (1, 2) in
slope-intercept form.
2 0 2m
1 ( 1) 21
= = =
Method #1y 0000 = 1111(x + 1111)
y = x + 1
Method #20000 = (1111)(1111) + b0 = 1 + b1 = b
y = x + 1
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7/30/2019 Obj. 3 Equations of Lines
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Graphing Lines Cut off the bottom edge of the foldable.
Fold the right edge over to the line.
Cut along the lines on the right side to the fold
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7/30/2019 Obj. 3 Equations of Lines
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Ex. Graph
Step 1: Plot the givenpoint
We are given the y-interceptso we put a point at (0, 3).
x
y
2y x 3
3= +
x
yStep 2: From thispoint, count the
rise upupupup if theslope is positiveand downdowndowndown if
theslope is negative.
Our slope is , so our rise
will be 2.
2
3
Graphing Lines
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Ex. Graph
Step 3: From this
new location,count the runto the rightrightrightright.
The run of our slope will be
3.
x
y
2y x 33
= +
x
yStep 4: Mark thispoint andconnect the twopoints.
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7/30/2019 Obj. 3 Equations of Lines
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A useful variation of the point-slope form
isolates the y variable by switching the y1value to the other
side:
y = m(x x1) + y
1
Example: Graph
Plot (3, 1)
Slope = 2
( )= +2 x 3 1
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7/30/2019 Obj. 3 Equations of Lines
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Pairs of LinesTwo lines will do one of three things:
Not intersect (parallel)
Intersect at one point
Intersect at all points (coincide)
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To determine which of these possibilities is true, look at
the slope and y-intercept:
To compare slopes and y-intercepts, put both equationsin
slope-intercept form (y=mx+b). If we do that to thelast equation,
we can see why the two coincide:
y 5 = 3(x 1)
y = 3x 3 + 5
y = 3x + 2
Parallel LinesParallel LinesParallel LinesParallel Lines
Intersecting LinesIntersecting LinesIntersecting LinesIntersecting
Lines Coinciding LinesCoinciding LinesCoinciding LinesCoinciding
Lines
y = 2x 9
y = 2x + 7
y = 3x + 5
y = 4x 1
y = 3x + 2
y 5 = 3(x 1)
same slope,differentintercept
different slopessame slope, same
intercept
