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Rate of Change

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  • 1. CHAPTER 6: Slopes and Lines
  • 2. RATE OF CHANGE
    • Lesson 6.1
  • 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. 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. 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. 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. 3 m 5 m Determine the rate of change ( pitch ) of the roof.
  • 12. Determine the rate of change of each staircase. 2 3 3 3
  • 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. 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
  • 21.  
  • 22. FORMULA FOR RATE OF CHANGE
    • y2 – y1
    • x2 – x1
    • The rate of change between points (x1, y1) and (x2, y2)