Rate of change
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CHAPTER 6: Slopes and Lines
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Essential Question How can you find the unit rate from a line on a graph that goes through the origin? Objective understand slope as it relates to rate of change
Transcript of Rate of change
CHAPTER 6:Slopes and Lines
RATE OF CHANGELesson 6.1
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 =
€
rise
run
RATES OF CHANGE ARE SEEN EVERYWHERE.
The steepness of the roof of a house is referred to as the pitch of the roof by home builders.
Give one reason why some homes have roofs which have a greater pitch.
There is less snow buildup in the wintertime.
Engineers refer to the rate of change of a road as the grade.
They often represent the rate of change as a percentage.
A grade of 8% would mean for every rise of 8 units there is a run of 100 units.
8100
= 8%
Rate of change = 8
100
The steepness of wheelchair ramps is of great importance for safety.
Rate of change of wheelchair ramp =
112
If the rise is 1.5 m, what is the run?
Answer: 18 m because
1
1 2
1
12
15
18= .
3 m
5 m
Determine the rate of change (pitch) of the roof.
3
5change of rate =
2
3
3
3
3
2
change of rate
=
3
3
change of rate
=
1=
Determine the rate of change of each staircase.
Determine the rate of change.Which points will you use to determine rise and run?
= $5/hr
run
rise
change of rate
=
hr 4
20 $=20
4
Earnings
Number of Hours Worked
What does this rate of change represent?
The hourly wage
RE
AL
LIF
E
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?
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
POSITIVE RATE OF CHANGE
At age 6 months, Joy weighed 15.75lbs. How fast did she grow from 4 months to 6
months?
Line Graph: Rate of Change
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…
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
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
FORMULA FOR RATE OF CHANGE
y2 – y1 x2 – x1 The rate of change between points (x1, y1)
and (x2, y2)
