Chapter 1.3, Problem 18AYU

In Problems 17-24, plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

$(-1,1);(2,3)$

To determine

To find: Plot the points $\left(-1,1\right)$ and $\left(2,3\right)$ and the slope of the line joining the point.

Answer to Problem 18AYU

Solution:

slope $\text{<mi>m</mi> = }\frac{2}{3}$, The rate change of $y$ with respect to $x$ is $\frac{2}{3}$.

Explanation of Solution

Given:

The points $\text{(−1, 1)}$ , $\left(2,3\right)$

Formula Used:

Slope $\text{<mi>m</mi> = }\frac{y_2-y_1}{x_2-x_1}$

Calculation:

The slope $m$ of the line containing the points $\text{(−1, 1)}$ and $\text{(2, 3)}$ is

$\text{<mi>m</mi> }= \frac{3-1}{2-\left(-1\right)}$

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

$= \frac{2}{3}$

For every 3 unit change in $x$ , $y$ will change by 2 units.

That is if $x$ increases by 3 units then $y$ will increase by by 2 units. The average rate of change of $y$ with respect to $x$ is $\frac{2}{3}$