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