Chapter 8.7, Problem 23E

To determine

To write:

A linear function g whose graph passes through the originand is parallel to the graph of givenfunction.

Answer to Problem 23E

The graph of function $g(x)=-8x$ is parallel to our given function.

Explanation of Solution

Given:

A function: $f(x)=-8x-2$ .

Concept used:

We know that the slopes of two parallel lines are same.

The equation of a line in slope-intercept form is $y=mx+b$ , where m represents slope of line and b represents the y -intercept.

Calculation:

We can see from our given function that it is in slope-intercept form and its slope is $-8$ . So, the slope of parallel line to our given line will be $-8$ .

Now we will substitute the slope and y -intercept $\left(0,0\right)$ in slope-intercept form of equation as:

  $\begin{array}{l}y=mx+b\left(\text{Slope-intercept form of equation}\right)\\ y=-8\cdot x+0\left(\text{Substituting }m=-8\text{ and }b=0\right)\\ y=-8x\\ g(x)=-8x\left(\text{Rewriting in function form}\right)\end{array}$

Therefore, the graph of function

  $g(x)=-8x$ is parallel to our given function.