4.7 Parallel and Perpendicular Lines
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Transcript 4.7 Parallel and Perpendicular Lines
4.7 Parallel and Perpendicular Lines
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
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!
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 x4
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
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