1. 5.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Write Equations of Parallel and Perpendicular Lines

2. 5.5 Warm-Up Are the lines parallel? Explain. 2. –x = y + 4, 3x + 3y = 5 ANSWER 1.y – 2 = 2x, 2x + y = 7 Yes; both slopes are –1. No; one slope is 2 and the other is –2.

3. 5.5 Warm-Up ANSWER $6 3. You play tennis at two clubs. The total cost C (in dollars) to play for time t (in hours) and rent equipment is given by C = 15t + 23 at one club and C = 15t + 17 at the other. What is the difference in total cost after 4 hours of play?

4. 5.5 Example 1 SOLUTION Write an equation of the line that passes through (–3, –5) and is parallel to the line y = 3x – 1. STEP 1 Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (–3, –5) has a slope of 3.

5. 5.5 Example 1 STEP 2 Find the y- intercept. Use the slope and the given point. y = mx + by = mx + b –5 = 3(–3) + b 4 = b Write slope-intercept form. Substitute 3 for m,  3 for x, and  5 for y. Solve for b. STEP 3 Write an equation. Use y = mx + b. y = 3x + 4 Substitute 3 for m and 4 for b.

6. 5.5 Guided Practice 1. Write an equation of the line that passes through (–2, 11 ) and is parallel to the line y = –x + 5. y = –x + 9 ANSWER

7. 5.5 Example 2 Determine which lines, if any, are parallel or perpendicular. Line a: y = 5x – 3 Line b: x + 5y = 2 Line c: –10y – 2x = 0 SOLUTION Find the slopes of the lines. Line a: The equation is in slope-intercept form. The slope is 5. Write the equations for lines b and c in slope-intercept form.

8. 5.5 Example 2 Line b: x + 5y = 2 5y = – x + 2 Line c: –10y – 2x = 0 –10y = 2x y = – x 1 5 x 2 5 1 5 + – ANSWER Lines b and c have slopes of –, so they are parallel. Line a has a slope of 5, the negative reciprocal of –, so it is perpendicular to lines b and c. 1 5 1 5

9. 5.5 Guided Practice Determine which lines, if any, are parallel or perpendicular. Line a: 2x + 6y = –3 Line b: y = 3x – 8 Line c: –1.5y + 4.5x = 6 ANSWER parallel: b and c ; perpendicular: a and b, a and c

10. 5.5 Example 3 SOLUTION Line a: 12y = –7x + 42 Line b: 11y = 16x – 52 Find the slopes of the lines. Write the equations in slope-intercept form. The Arizona state flag is shown in a coordinate plane. Lines a and b appear to be perpendicular. Are they ? STATE FLAG

11. 5.5 Example 3 Line a: 12y = –7x + 42 Line b: 11y = 16x – 52 y = –y = – x + 12 42 7 12 11 52 y = x – 16 11 ANSWER The slope of line a is –. The slope of line b is. The two slopes are not negative reciprocals, so lines a and b are not perpendicular. 7 12 16 11

12. 5.5 Guided Practice 3. Is line a perpendicular to line b? Justify your answer using slopes. Line a: 2y + x = –12 Line b: 2y = 3x – 8 ANSWER No; the slope of line a is –, the slope of line b is. The slopes are not negative reciprocals so the lines are not perpendicular. 1 2 3 2

13. 5.5 Example 4 SOLUTION Write an equation of the line that passes through (4, –5) and is perpendicular to the line y = 2x + 3. STEP 1 Identify the slope. The graph of the given equation has a slope of 2. Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line through (4, –5) is. 1 2 –

14. 5.5 Example 4 STEP 2 Find the y- intercept. Use the slope and the given point. Write slope-intercept form. –5 = – (4) + b 1 2 Substitute – for m, 4 for x, and – 5 for y. 1 2 y =y = mx + bmx + b –3 = b Solve for b. STEP 3 Write an equation. y = mx + b Write slope-intercept form. y = – x – 3 1 2 Substitute – for m and –3 for b. 1 2

15. 5.5 Guided Practice 4. Write an equation of the line that passes through (4, 3) and is perpendicular to the line y = 4x – 7. y = – x + 4 1 4 ANSWER

16. 5.5 Lesson Quiz 1. Write an equation of the line that passes through the point (–1, 4) and is parallel to the line y = 5x – 2. y = 5x + 9 ANSWER Write an equation of the line that passes through the point (–1, –1) and is perpendicular to the line y = x + 2. 1 4 – 2. y = 4x + 3 ANSWER

17. 5.5 Lesson Quiz 3. Path a, b and c are shown in the coordinate grid. Determine which paths, if any, are parallel or perpendicular. Justify your answer using slopes. ANSWER Paths a and b are perpendicular because their slopes, 2 and are negative reciprocals. No paths are parallel. 1 2 –