Chapter 8.7, Problem 2E

To determine

To describe:

How can you find the slope of graph of f ?

Answer to Problem 2E

The slope of the line passing through the given points would be $-\frac{3}{2}$ .

Explanation of Solution

Given:

Suppose f is a linear function with $f(2)=5,f(6)=-1$ .

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 $(2,5)\text{and }(6,-1)$ .

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

Let point $(2,5)=(x_1,y_1)\text{and }(6,-1)=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-1-5}{6-2}\\ m=\frac{-6}{4}\\ m=-\frac{3}{2}\end{array}$

Therefore, the slope of the line passing through the given points would be $-\frac{3}{2}$ .