# ALGEBRA 1 LESSON 6 1 Rate of Change

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope (For help, go to Lessons 5 -2 and 1 -5. ) Evaluate each function rule for x = – 5. 1. y = x – 7 2. y = 7 – x 3. y = 2 x + 5 2 4. y = – x + 3 5 Write in simplest form. 5. 7– 3 3– 1 8. – 1 – 2 0– 5 6. 3– 5 6– 0 9. – 6 – (– 4) – 2 – 6 8 -3 7. 8 – (– 4) 3– 7 10. 0 – 1 1– 0

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope 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 100 Fee $30 150 $42 200 $54 250 $66 Find the rate of change for each pair of consecutive mileage amounts. 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope (continued) rate of change = change in cost change in number of miles 42 – 30 12 = 150– 100 50 54 – 42 12 = 200– 150 50 Cost depends on the number of miles. 66 – 54 12 = 200– 250 50 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. 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope 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. Choose two points On the graph (0, 0) and (400, 20) 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope (continued) Using the points (0, 0) and (400, 20), find the rate of change = = vertical change horizontal change 400 – 0 change in distance change in time Use two points. 20 – 0 Divide the vertical change by the horizontal change. 400 20 Simplify. 20 The rate of change is 20 m/s. The motorcycle is traveling 20 meters each second. 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope Find the slope of each line. a. slope = rise run = 4– 1 0– 2 = 3 – 2 =– 3 2 The slope of the line is – 3. 2 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope (continued) b. Find the slope of the line. slope = = rise run – 1 – 2 – (– 2) = – 2 – 1 = 2 The slope of the line is 2. 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope Find the slope of each line through E(3, – 2) and F(– 2, – 1). y 2 – y 1 slope = x 2 – x 1 = – 1 – (– 2) Substitute (– 2, – 1) for (x 2, y 2) and (3, – 2) for (x 1, y 1). – 2 – 3 = – 51 Simplify. = – 15 The slope of EF is – 1. 5 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope Find the slope of each line. a. slope = = y 2 – y 1 x 2 – x 1 2– 2 1 – (– 4) = 0 5 Substitute (1, 2) for (x 2, y 2) and (– 4, 2) for (x 1, y 1). Simplify. = 0 The slope of the horizontal line is 0. 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope (continued) b. Find the slope of the line. y –y slope = x 2 – x 1 2 1 = 1 – (– 4) Substitute (2, 1) for (x 2, y 2) and (2, – 4) for (x 1, y 1). = 5 Simplify. 2– 2 0 Division by zero is undefined. The slope of the vertical line in undefined. 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope 1. Find the rate of change 2. Find the rate of change 3. Find the slope of the line. for the data in the table. for the data in the graph. Tickets Cost 5 6 7 8 $75 $90 $105 $120 4. Find the slope of the line through (3, – 2) and (– 2, 5). 8 -3

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope 5. State whether the slope is zero or undefined. a. b. 8 -3

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

ALGEBRA 1 LESSON 6 -1 Rate of Change and Slope 5. State whether the slope is zero or undefined. a. b. undefined 0 8 -3

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