Perpendicular Line Through a Given Point

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• Write an equation of the line that passes through a
given point, parallel to a given line.
• Write an equation of the line that passes through a
given point, perpendicular to a given line.
• parallel lines
• perpendicular lines
Parallel Line Through a Given Point
Write the slope-intercept form of an equation for
the line that passes through (4, –2) and is parallel to
the graph of
Parallel Line Through a Given Point
Point-slope form
Replace m with
y with –2, and x with 4.
Simplify.
Distributive Property
Subtract 2 from each side
Parallel Line Through a Given Point
Write the equation in slopeintercept form.
Answer: The equation is
Write the slope-intercept form of an equation for the
line that passes through (2, 3) and is parallel to the
graph of
A.
B.
0%
D
A
0% B
C
D
C
D.
A
0%
A.
0%B.
C.
D.
B
C.
Determine Whether Lines are
Perpendicular
GEOMETRY The height of a
trapezoid is measured on a
segment that is perpendicular
to a base. In trapezoid ARTP,
RT and AP are bases. Can EZ
be used to measure the
height of the trapezoid?
Explain.
Determine Whether Lines are
Perpendicular
Find the slope of each segment.
Determine Whether Lines are
Perpendicular
Answer: The slope of RT and AP is 1 and the slope of
EZ is –7. –7●1  –1. EZ is not perpendicular to RT and
AP, so it cannot be used to measure height.
The graph shows the
diagonals of a rectangle.
Determine whether JL is
perpendicular to KM.
A. JL is not perpendicular to KM.
1.
2.
3.
A
0%
0%
B
C. Cannot be determined
A
B
C
0%
C
B. JL is perpendicular to KM.
Perpendicular Line Through a Given Point
Write the slope-intercept form for an equation of a
line that passes through (4, –1) and is
perpendicular to the graph of 7x – 2y = 3.
Step 1 Find the slope of the given line.
7x – 2y = 3
7x – 2y – 7x = 3 – 7x
–2y = –7 + 3
Original equation
Subtract 7x from each
side.
Simplify.
Perpendicular Line Through a Given Point
Divide each side by –2.
Simplify.
Step 2
Perpendicular Line Through a Given Point
Step 3 Use the point-slope form to find the equation.
Point-slope form
Simplify.
Distributive Property
Perpendicular Line Through a Given Point
Subtract 1 from each side.
Simplify.
Answer: The equation of the line is
Write the slope-intercept form for an equation of
a line that passes through (–3, 6) and is
perpendicular to the graph of 3x + 2y = 6.
A.
B.
C.
D.
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Perpendicular Line Through a Given Point
Write the slope-intercept form for an equation of a
line perpendicular to the graph of 2y + 5x = 2 that
passes through (0, 6).
Step 1 Find the slope of 2y + 5x = 2.
2y + 5x = 2
2y + 5x – 5x = 2 – 5x
2y = –5x + 2
Original equation
Subtract 5x from each
side.
Simplify.
Perpendicular Line Through a Given Point
Divide each side by 2.
Simplify.
Step 2
Perpendicular Line Through a Given Point
Step 3 Substitute the slope and the given point into
the point-slope form of a linear equation. Then
write the equation in slope-intercept form.
Point-slope form
Distributive Property
Answer: The equation of the line is
Write the slope-intercept form for an equation of
a line perpendicular to the graph of y = 2x + 1 that
passes through the x-intercept of that line.
A.
B.
D.
A
B0%
C
D
D
0%
B
A
0%
A.
B.0%
C.
D.
C
C.

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