4.7 Parallel and Perpendicular Lines

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4.7 Parallel and Perpendicular Lines
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Parallel lines have the same slope.
All vertical lines are parallel.
All horizontal lines are parallel.
Perpendicular lines have opposite reciprocal
slopes.
If m = 3, then the m = -1/3
If m = -2/3, then the m = 3/2
Write an equation of the line that is
parallel to the graph of 2x + y = 5 and
passes through the point (3,1).
2x  y  5
y  2 x  5
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Since y  m x  b the slope is -2.
Using the point (3,1) and the parallel slope of -2,
plug all into the point-slope form y  y  m( x  x )
1
1
y  1  2( x  3)
y  1  2 x  6
Distribute
Add 1 to both sides
y  2 x  7
Write an equation of the line that is
perpendicular to the graph of x - 6y = 2
and passes through the point (2,4).
x  6y  2
 6 y  x  2
1
1
y  x
6
3
1
m
6
 m  6
Use pointslope form
with slope = -6
and point
given (2,4)
y  y1  m( x  x1 )
y  4  6( x  2)
y  4  6 x  12
y  6 x  16
Try These Two to Practice!
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Write the slope-intercept form of an equation
for the line that passes through (4,-2) and is
parallel to the graph of y  1 x  7
2
1
y  x4
2
Write the slope-intercept for of an equation
for the line that passes through (4,-1) and is
perpendicular to the graph of 7 x  2 y  3
2
1
y  x
7
7
Page 239 #1-7 odd
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1. y = -2x -1
3. y = 2x – 5
5. Find the slope of segment AC
6/7
Find the slope of segment BD
-7/6
They are opposite reciprocal slopes therefore
they are perpendicular.
7. y   5 x  8
3
Homework #33: p. 240 10-30, 36, 37

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