Chapter 2.3, Problem 2AYU

‘Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

2. The slope of the line containing the points $\left(-2,3\right)$ and $\left(3,8\right)$ is ______. (pp. 30-32)

To determine

To fill: The slope of the line containing the points $\left(-2,3\right)$ and $\left(3,8\right)$.

Answer to Problem 2AYU

The slope of the line containing the points $\left(-2,3\right)$ and $\left(3,8\right)$ is 1.

Explanation of Solution

By the definition slope of the line containing two points, let $P=\left(x_1,y_1\right)$ and $Q=\left(x_2,y_2\right)$ be two distinct points. If $x_1\ne x_2$, the slope $m$ of the nonvertical line $L$ containing $P$ and $Q$ is defined by the formula $m=\frac{y_2-y_1}{x_2-x_1}$   $x_1\ne x_2$.

If $x_1=x_2$, $L$ is vertical line and the slope $m$ of $L$ is undefined (since this results in division by 0).

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3+2}{8-3}=\frac{5}{5}=1$