lesson 7 mi/vocab parallel lines perpendicular lines write an equation of the line that passes...
TRANSCRIPT
• parallel lines
• perpendicular lines
• 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 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
Simplify.
Distributive Property
Subtract 2 from each side
Replace m with
y with –2, and x with 4.
Parallel Line Through a Given Point
Write the equation in slope-intercept form.
Answer: The equation is
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
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.
C.
D.
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.
Find the slope of each segment.
Determine Whether Lines are Perpendicular
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.
1. A
2. B
3. C
0% 0%0%
The graph shows the diagonals of a rectangle. Determine whether JL is perpendicular to KM.
A. JL is not perpendicular to KM.
B. JL is perpendicular to KM.
C. Cannot be determined
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.
Original equation
Subtract 7x from each side.
Simplify.
7x – 2y = 3
–2y = –7 + 3
7x – 2y – 7x = 3 – 7x
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
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
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.
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.
Perpendicular Line Through a Given Point
Original equation
Subtract 5x from each side.
Simplify.
2y + 5x = 2
2y = –5x + 2
2y + 5x – 5x = 2 – 5x
Perpendicular Line Through a Given Point
Divide each side by 2.
Simplify.
Step 2
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.
Perpendicular Line Through a Given Point
Point-slope form
Distributive Property
Answer: The equation of the line is
A. A
B. B
C. C
D. D
A B C D
0% 0%0%0%
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.
C.
D.