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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)