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# Rate of Change

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### Rate of Change

1. 1. CHAPTER 6: Slopes and Lines
2. 2. RATE OF CHANGE <ul><li>Lesson 6.1 </li></ul>
3. 3. RATE OF CHANGE OF A LINEAR RELATIONSHIP The rate of change of a linear relationship is the steepness of the line. rise run Rate of Change =
4. 4. RATES OF CHANGE ARE SEEN EVERYWHERE.
5. 5. The steepness of the roof of a house is referred to as the pitch of the roof by home builders.
6. 6. Give one reason why some homes have roofs which have a greater pitch . There is less snow buildup in the wintertime.
7. 7. Engineers refer to the rate of change of a road as the grade .
8. 8. They often represent the rate of change as a percentage .
9. 9. A grade of 8% would mean for every rise of 8 units there is a run of 100 units . = 8% 8 100 Rate of change =
10. 10. The steepness of wheelchair ramps is of great importance for safety. Rate of change of wheelchair ramp = 1 12 If the rise is 1.5 m, what is the run? Answer: 18 m because
11. 11. 3 m 5 m Determine the rate of change ( pitch ) of the roof.
12. 12. Determine the rate of change of each staircase. 2 3 3 3
13. 13. Determine the rate of change. Which points will you use to determine rise and run? = \$5/hr 20 4 Earnings Number of Hours Worked What does this rate of change represent? The hourly wage
14. 14. REAL LIFE <ul><li>Mr. and Mrs. Overjoyed had a healthy baby girl named Joy who weighed 7.5lbs. at birth. At the end of 4 months, the baby weighed 13.5lbs. </li></ul><ul><li>How fast did her weight change from birth to 4 months? </li></ul>
15. 15. REAL LIFE (PART 2) <ul><li>To answer this question, we calculate the Rate of Change of Joy’s weight, that is, how much she gained per month. </li></ul><ul><li>Change in weight 13.5lbs – 7.5lbs 6lbs </li></ul><ul><li>Change in age 4mo – 0mo 4mo </li></ul><ul><li>1.5lbs./month </li></ul>
16. 16. POSITIVE RATE OF CHANGE <ul><li>At age 6 months, Joy weighed 15.75lbs. </li></ul><ul><li>How fast did she grow from 4 months to 6 months? </li></ul>
17. 17. Line Graph: Rate of Change
18. 18. NEGATIVE RATE OF CHANGE <ul><li>Joy was gaining weight, so the rate of change was positive. But a rate of change can be negative. </li></ul><ul><li>Let’s take a look at the population of Chicago from 1830 to 2000… </li></ul>
19. 19. <ul><li>The rate of change, in people per year, from 1890 to 1900. For these years, the population increased. </li></ul><ul><li>Change in population 1,698,575 – 1,099,850 598,725p </li></ul><ul><li>Change in years 1900 – 1890 10yr </li></ul><ul><li>59, 872.5 people/year </li></ul>
20. 20. <ul><li>Between 1970 and 1980 the population decreased, so the rate of change is negative. </li></ul><ul><li>Change in population 3,005,072 – 3,369,357 -364, 285 p </li></ul><ul><li>Change in years 1980 - 1970 10 years </li></ul><ul><li>- 36,428.5 people per year </li></ul>
21. 22. FORMULA FOR RATE OF CHANGE <ul><li>y2 – y1 </li></ul><ul><li>x2 – x1 </li></ul><ul><li>The rate of change between points (x1, y1) and (x2, y2) </li></ul>