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Algebra 1

4.8.4 Rate of Change of Linear Functions

Algebra 14.8.4 Rate of Change of Linear Functions

4.8.4 Rate of Change of Linear Functions

4.8.4 • Rate of Change of Linear Functions

Activity

Three people, Adam, Bianca, and Carmen, are competing to see who can save the most money in one month. Use the table, graph, and equation below to answer the questions.

1. Use the graph to find the average rate of change of the function that represents Adam’s savings for the following intervals:

a. between 0 and 1 days

b. between 1 and 2 days

c. between 1 and 3 days

2. Use the table to find the average rate of change for the function that represents Bianca’s savings for the following intervals:

a. between 5 and 8 days

b. between 12 and 20 days

c. between 5 and 20 days

3. Use the equation to find the average rate of change for the function that represents Carmen’s savings for the following intervals:

a. between 1 and 2 days

b. between 2 and 4 days

c. between 1 and 4 days

4. Which statements are true?

  1. All three functions are linear functions.
  2. All three functions have the same rate of change.
  3. All three functions have a constant rate of change.

5. Who has the most money after 30 days? Explain how you know.

Self Check

What is the average rate of change for the linear function?

Input Output
1 2
2 -1
4 -7
6 -13
  1. 1 3
  2. − 1 3
  3. − 3
  4. 3

Additional Resources

Rate of Change of Linear Functions.

 The graph of a linear function is identical to the graph of the linear equation that describes it. The rate of change of a linear equation is constant. The rate of change is the slope, m=y2−y1x2−x1m=y2−y1x2−x1

  1. Find the rate of change of a linear function from a graph.

The rate of change of a linear function is constant, so you can choose any 2 points to find the slope.

Use (16,1)(16,1) and (24,1.5)(24,1.5).

m=y2−y1x2−x1=1.5−124−16=0.58=116m=y2−y1x2−x1=1.5−124−16=0.58=116

The rate of change is 116116

2. Find the rate of change of a linear function from a table.

Input Output
-2 3
8 -2
10 -3
20 -8

The rate of change of a linear function is constant, so you can choose any 2 points to find the slope.

Use (−2,3)(−2,3) and (8,−2)(8,−2).

m=y2−y1x2−x1=−2−38−(−2)=−510=−12m=y2−y1x2−x1=−2−38−(−2)=−510=−12

The rate of change is −12−12.

3. Find the rate of change of a linear function from an equation.

F(x)=7x+6F(x)=7x+6

Use the slope intercept form, y=mx+by=mx+b, where mm is the slope and bb is the yy-intercepts.

y=7x+6y=7x+6

The slope is 7. The rate of change is 7.

Try it

Try It: Rate of Change of Linear Functions

The function V(x)V(x) gives the volume of water that flows from a faucet in gallons during 𝒙𝒙 minutes. V(x)V(x) is a linear function with the graph shown.What is the rate of change of the volume?

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