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Chapter 3: Q. 4 (page 173)

In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

Short Answer

Expert verified

The function is linear and the equation of the line is y=5x+3.

Step by step solution

01

Step 1. Given information.

Determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

02

Step 2. Equation of line and slope of the graph.

The linear function is given by

g(x)=mx+b;m≠0

The slope of the graph is mand the y-intercept is b.The average rate of change is equal to the slope.

localid="1646321689835" m=gx2-gx1x2-x1

The linear function have a constant average rate of change.

03

Step 3. find linear function.

Look at the given table and notice that

y5-y4=y4-y3=y3-y2=y2-y1=5.

When you changes x value for 1. So, average rate of change is constant. Then the slope is m=5.

Also the y-intercept is b=3because that is the value of the function for x=0.

Then the equation of function is:

f(x)=5x+3

04

Step 4. Conclusion. 

The function is linear and the equation of line is f(x)=5x+3.

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Most popular questions from this chapter

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.

xy=f(x)
-2-8
-1-3
00
11
20

Show that the inequality (x-2)2>0has one real number that is not a solution.

Match each graph to one the following functions.

f(x)=x2-2x+1

In Problems 7–22, solve each inequality.

4x2+9<6x

If f(x)=2x+3, then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant
See all solutions

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