1. 5-1 Rate of Change and Slope Hubarth Algebra

2. Rate of change allows you to see the relationship between two quantities that are changing. If one quantity depends on the other, then the following is true. Ex 1 Finding Rate of Change Using a Table Find the rate of change for each pair of consecutive mileage amounts. For the data in the table, is the rate of change the same for each pair of consecutive mileage amounts? Fee for Miles Driven MilesFee 100$30 150 200 250 $42 $54 $66 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. change in costCost 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 ===,,

3. 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. Ex 2 Finding Rate of Change Using a Graph The rate of change is 20 m/s. The motorcycle is traveling 20 meters each second. vertical change change in distance horizontal change change in time rate of change = 400 – 0 20 – 0 = Use two points. = Simplify. 20 = Divide the vertical change by the horizontal change. 400 20

4. Finding Slope Ex 3 Finding the Slope Using a Graph slope = rise run Find the slope of each line. a. 4 – 1 0 – 2 = = 3 –2 = – 3232 The slope of the line is –. 3232 The slope of the line is 2. slope = rise run b. = 2 –1 – 1 –2 – (–1) = = –2 –1

5. slope = y 2 – y 1 x 2 – x 1 The slope of EF is –. 1515 Find the slope of the line through E(3, –2) and F(–2, –1). Substitute (–2, –1) for (x 2, y 2 ) and (3, –2) for (x 1, y 1 ). – 1 – (–2) –2 – 3 = = – 1515 = 1 –5 Simplify. Ex 4 Finding Slope Using Points

6. = 0 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 The slope of the horizontal line is 0. Find the slope of each line. a. = 0 5 Simplify. Ex 5 Horizontal and Vertical Lines Division by zero is undefined. The slope of the vertical line is undefined. b. 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

7. Summary Slope of Lines A line with a Positive slope slants upward from left to right A line with a negative slope slants downward from left to right A line with a slope of 0 is horizontal A line with an undefined slope is vertical. if the denominator is 0, then the slope is undefined

8. Practice 1. Find the slope of a line passing through the points a. (3, 4) and (-2, 3)b. (-2, 5) and (-3, 6) c. (1, 6) and (2, 3)d. (4, -1) and (5, 3) 2. Find the slope from the given graphs.. (2, 2). (-1, 0) a. b. c. m=0undefined