Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The equation of line is nonlinear.

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.

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

The linear function have a constant average rate of change.

Step 3. find linear function.

Look at the given table and notice that 

$y_5-y_4\ne y_4-y_3\iff 1-(-6)\ne 6-7\iff 7\ne -1$

When you changes x value for 1. So, average rate of change is not constant.

So this is non linear.

Step. Conclusion.

The equation of line is nonlinear.