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Expert-verified Found in: Page 173 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line. The function is linear and the equation of the line is $y=5x+3$.

See the step by step solution

## Step 1. Given information.

Determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line. ## Step 2. Equation of line and slope of the graph.

The linear function is given by

$g\left(x\right)=mx+b;m\ne 0$

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

localid="1646321689835" $m=\frac{g\left({x}_{2}\right)-g\left({x}_{1}\right)}{{x}_{2}-{x}_{1}}$

The linear function have a constant average rate of change.

## Step 3. find linear function.

Look at the given table and notice that

${y}_{5}-{y}_{4}={y}_{4}-{y}_{3}={y}_{3}-{y}_{2}={y}_{2}-{y}_{1}=5$.

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 $b=3$ because that is the value of the function for $x=0$.

Then the equation of function is:

$f\left(x\right)=5x+3$

## Step 4. Conclusion.

The function is linear and the equation of line is $f\left(x\right)=5x+3$. ### Want to see more solutions like these? 