Chapter 8.7, Problem 43E

To determine

Suppose f is a linear function with $g(-3)=28,g(0)=4$ . What is the slope of graph of g ?

Answer to Problem 43E

The slope of graph of g would be $-8$ and option F is the correct choice.

Explanation of Solution

Given:

Four choices: $\text{F}\text{.}-8\text{ G}\text{.}-\frac{1}{8}\text{ H}\text{. }\frac{1}{8}\text{ D}\text{. 8}$

Concepts used:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1},\text{where,}\\ m=\text{Slope of line,}\\ y_2-y_1=\text{Difference between two }y\text{-coordinates}\\ x_2-x_1=\text{Difference between two }x\text{-coordinates of same }y-\text{coordinates}\end{array}$

Calculation:

We can see that the given inputs and outputs of function represent two points on a line that are $(-3,28)\text{and }(0,4)$ .

Now we will find the slope of line passing through the given points using slope formula.

Let point $(-3,28)=(x_1,y_1)\text{and }(0,4)=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{4-28}{0-(-3)}\\ m=\frac{-24}{0+3}\\ m=-8\end{array}$

Therefore, the slope of graph of g would be $-8$ and option F is the correct choice.