1 / 8

5-1 Rate of Change and Slope

5-1 Rate of Change and Slope. Hubarth Algebra. change in cost Cost depends on the change in number of miles number of miles. rate of change =. Fee for Miles Driven. 42 – 30 12 54 – 42 12 66 – 54 12 150 – 100 50 200 – 150 50 250 – 200 50. =. =. =.

zaide
Download Presentation

5-1 Rate of Change and Slope

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. change in costCost depends on the change in number of milesnumber of miles. rate of change = Fee for Miles Driven 42 – 3012 54– 421266– 5412 150–10050 200–15050 250–200 50 = = = Miles Fee , , 100 $30 150 $42 200 $54 250 $66 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 For the data in the table, is the rate of change the same for each pair of consecutive mileage amounts? Find the rate of change for each pair of consecutive mileage amounts. 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.

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

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

  5. –1 – (–2) –2 – 3 = y2– y1 x2– x1 slope = Substitute (–2, –1) for (x2, y2) and (3, –2) for (x1, y1). Simplify. 1 –5 1 5 = = – 1 5 The slope of EF is – . Ex 4 Finding Slope Using Points Find the slope of the line through E(3, –2) and F(–2, –1).

  6. a. y2– y1 x2 – x1 slope = y2 –y1 x2–x1 slope = Substitute (1, 2) for (x2, y2) and (–4, 2) for (x1, y1). Substitute (2, 1) for (x2, y2) and (2, –4) for (x1, y1). 1 –(–4) 2 – 2 = 2 – 2 1– (–4) = Simplify. 5 0 = Simplify. 0 5 = Ex 5 Horizontal and Vertical Lines Find the slope of each line. The slope of the horizontal line is 0. = 0 b. Division by zero is undefined. The slope of the vertical line is undefined.

  7. Summary Slope of Lines A line with a negative slope slants downward from left to right A line with a Positive slope slants upward 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. a. b. c. . (2, 2) . (-1, 0) m=0 undefined

More Related