3. Rate of Change and Slope Evaluate each function rule for x = –5. 1. y = x – 7 2. y = 7 – x 3. y = 2 x + 5 4. y = – x + 3 Write in simplest form. 5. 6. 7. 8. 9. 10. 2 5 7 – 3 3 – 1 3 – 5 6 – 0 8 – (–4) 3 – 7 – 1 – 2 0 – 5 – 6 – (–4) – 2 – 6 0 – 1 1 – 0 (For help, go to Lessons 5-2 and 2-2.) Lesson 6-1 Check Skills You’ll Need 6-1 Ms. Ridgell 2010-11

4. Rate of Change and Slope 1. y = x – 7 for x = –5: y = –5 – 7 = –12 2. y = 7 – x for x = –5: y = 7 – (–5) = 12 3. y = 2 x + 5 for x = –5: y = 2(–5) + 5 = –10 + 5 = –5 4. y = – x + 3 for x = –5: y = – (–5) + 3 = 2 + 3 = 5 5. = = 2 6. = – = – 7. = – = –3 8. = = 9. = = 10. = – = –1 7 – 3 3 – 1 3 – 5 6 – 0 8 – (–4) 3 – 7 – 1 – 2 0 – 5 – 6 – (–4) – 2 – 6 0 – 1 1 – 0 2 5 2 5 4 2 2 6 1 3 12 4 – 2 – 8 1 4 1 1 – 3 – 5 3 5 Lesson 6-1 Solutions Check Skills You’ll Need 6-1 Ms. Ridgell 2010-11

5. Rate of Change and Slope Find the rate of change for each pair of consecutive mileage amounts. Lesson 6-1 Additional Examples 6-1 Ms. Ridgell 2010-11 For the data in the table, is the rate of change the same for each pair of consecutive mileage amounts? Fee for Miles Driven Miles Fee 100 $30 150 200 250 $42 $54 $66

6. Rate of Change and Slope The rate of change for each pair of consecutive mileage amounts is $12 per 50 miles. The rate of change is the same for all the data. (continued) Lesson 6-1 Quick Check Additional Examples 6-1 Ms. Ridgell 2010-11 change in cost Cost depends on the change in number of miles number of miles. rate of change = 42 – 30 12 54 – 42 12 66 – 54 12 150 – 100 50 200 – 150 50 250 – 200 50 = = =

7. Rate of Change and Slope Choose two points On the graph ( 0 , 0 ) and ( 400 , 20 ) Lesson 6-1 Additional Examples 6-1 Ms. Ridgell 2010-11 Below is a graph of the distance traveled by a motorcycle from its starting point. Find the rate of change. Explain what this rate of change means.

8. Rate of Change and Slope The rate of change is 20 m/s. The motorcycle is traveling 20 meters each second. (continued) Using the points ( 0 , 0 ) and ( 400 , 20 ), find the rate of change. Lesson 6-1 Quick Check Additional Examples 6-1 Ms. Ridgell 2010-11 vertical change change in distance horizontal change change in time rate of change = 400 – 0 20 – 0 = Use two points. = Divide the vertical change by the horizontal change. 400 20 = Simplify. 20

9. Rate of Change and Slope Find the slope of each line. Lesson 6-1 Additional Examples 6-1 Ms. Ridgell 2010-11 The slope of the line is – . 3 2 slope = rise run a. = – 3 2 = 3 – 2 4 – 1 0 – 2 =

10. Rate of Change and Slope The slope of the line is 2. (continued) = 2 Lesson 6-1 Quick Check Additional Examples 6-1 Ms. Ridgell 2010-11 slope = rise run b. Find the slope of the line. = – 2 – 1 – 1 – 1 – 2 – ( –2 ) =

11. Rate of Change and Slope Lesson 6-1 Quick Check Additional Examples 6-1 Ms. Ridgell 2010-11 slope = y 2 – y 1 x 2 – x 1 The slope of EF is – . 1 5 Find the slope of each line through E (3, –2) and F (–2, –1). = – 1 5 Substitute (–2, –1) for ( x 2 , y 2 ) and (3, –2) for ( x 1 , y 1 ). – 1 – ( –2 ) – 2 – 3 = = 1 – 5 Simplify.

12. Rate of Change and Slope = 0 The slope of the horizontal line is 0. Lesson 6-1 Additional Examples 6-1 Ms. Ridgell 2010-11 2 – 2 1 – ( –4 ) = Substitute (1, 2) for ( x 2 , y 2 ) and (–4, 2) for ( x 1 , y 1 ). slope = y 2 – y 1 x 2 – x 1 Find the slope of each line. a. = 0 5 Simplify.

13. Rate of Change and Slope Division by zero is undefined. The slope of the vertical line in undefined. b. (continued) Find the slope of the line. Lesson 6-1 Quick Check Additional Examples 6-1 Ms. Ridgell 2010-11 Substitute (2, 1) for ( x 2 , y 2 ) and (2, –4) for ( x 1 , y 1 ). = 1 – ( –4 ) 2 – 2 = 5 0 Simplify. slope = y 2 – y 1 x 2 – x 1

14. Rate of Change and Slope $15 per ticket 400 calories per hour 4 3 1. Find the rate of change for the data in the table. 2. Find the rate of change for the data in the graph. 3. Find the slope of the line. 4. Find the slope of the line through (3, –2) and (–2, 5). Lesson 6-1 Lesson Quiz 6-1 Ms. Ridgell 2010-11 7 5 – 5 $75 6 7 8 $90 $105 $120 Tickets Cost

15. Rate of Change and Slope undefined 0 Lesson 6-1 Lesson Quiz 6-1 Ms. Ridgell 2010-11 5. State whether the slope is zero or undefined. a. b.