Chapter 1.3, Problem 14AYU

In Problems 13-16, (a) find the slope of the line and (b) interpret the slope.

To determine

To find: The slope of the given points and interpreting the slope

Answer to Problem 14AYU

Solution:

slope $m = \frac{1}{3}$, The rate change of $y$ with respect to $x$ is $\frac{1}{3}$.

Explanation of Solution

Given:

The following fig

Formula Used:

Slope $m = \frac{y_2-y_1}{x_2-x_1}$

Calculation:

The slope $m$ of the line containing the points $\left(-1,1\right)$ and $\text{(2, 2)}$ is

$\text{<mi>m</mi> = }\frac{2-1}{2-\left(-1\right)}$

$= \frac{1}{2+1}$

$= \frac{1}{3}$

For every 3 units change in $x$, $y$ will change by 1 unit.

That is if $x$ increases by 3 units then $y$ will increase by 1 unit. The average rate of change of $y$ with respect to $x$ is $\frac{1}{3}$