Question

Determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.

Short answer

The function is linear and the equation of the line is$f\left(x\right)=-5x+2$.

Step-by-step solution

Step 1. Given information.

Determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.

Step 2. 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 mand the y-intercept is b.The average rate of change is equal to the slope.

$m=\frac{g\left(x_2\right)-g\left(x_1\right)}{x_2-x_1}$

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 $b=2$because that is the value of the function for $x=0$.

Then the equation of function is:

$f\left(x\right)=-5x+2$

Step 4. Conclusion.

The function is linear and the equation of line is$f\left(x\right)=-5x+2$.