Chapter 3.1, Problem 2AYU

Find the slope of the line joining the points $\left(2,5\right)$ and $\left(-1,3\right)$. (pp. 30-31)

To determine

The slope of the given line.

Answer to Problem 2AYU

Solution:

The slope of the given line is $\frac{2}{3}$.

Explanation of Solution

Given:

The given line joins the points $(2,5)$ and .

Formula Used:

The slope of a function is the average rate of change of the given function.

Therefore, the slope, $m$, of the line is the ratio of the change in the $y\text{-axis}$ to the change in the $x\text{-axis}$.

Thus, we have

$m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Thus, using the above formula, we get the slope of the given line as

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

$\begin{array}{l}=\frac{3-5}{-1-2}\\ = \frac{-2}{-3}\end{array}$

$=\frac{-2}{-3}$

$=\frac{2}{3}$