1. Lesson 7 MI/Vocab 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.

2. Lesson 7 Key Concept 1

3. Lesson 7 Ex1 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

4. Lesson 7 Ex1 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.

5. Lesson 7 Ex1 Parallel Line Through a Given Point Write the equation in slope- intercept form. Answer: The equation is

6. A.A B.B C.C D.D Lesson 7 CYP1 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.

7. Lesson 7 Key Concept 2

8. Lesson 7 Ex2 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.

9. Lesson 7 Ex2 Find the slope of each segment. Determine Whether Lines are Perpendicular

10. Lesson 7 Ex2 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.

11. 1.A 2.B 3.C Lesson 7 CYP2 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

12. Lesson 7 Ex3 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 1Find 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

13. Lesson 7 Ex3 Perpendicular Line Through a Given Point Divide each side by –2. Simplify. Step 2

14. Lesson 7 Ex3 Perpendicular Line Through a Given Point Step 3Use the point-slope form to find the equation. Point-slope form Simplify. Distributive Property

15. Lesson 7 Ex3 Perpendicular Line Through a Given Point Subtract 1 from each side. Simplify. Answer: The equation of the line is

16. 1.A 2.B 3.C 4.D Lesson 7 CYP3 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.

17. Lesson 7 Ex4 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 1Find 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

18. Lesson 7 Ex4 Perpendicular Line Through a Given Point Divide each side by 2. Simplify. Step 2

19. Lesson 7 Ex4 Step 3Substitute 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

20. A.A B.B C.C D.D Lesson 7 CYP4 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.