Chapter 13.7, Problem 12CE

To determine

To state : the slope of the line and name two points on the line

Answer to Problem 12CE

The slope of the line is $\frac{1}{2}$ and the two points are $\left(0,-\frac{9}{2}\right)$ , $\left(1,-4\right)$

Explanation of Solution

Given information :

  $y+2=\frac{1}{2}\left(x-5\right)$

Formula used :

  $y=mx+b$

Calculation :

The value of $y$

  $\begin{array}{l}y+2=\frac{1}{2}\left(x-5\right)\\ y=\frac{1}{2}x-\frac{5}{2}-2\\ y=\frac{1}{2}x-\frac{9}{2}\end{array}$

Let the slope of the line $=m$

The equation is $y=\frac{1}{2}x-\frac{9}{2}$

Therefore, the slope of the line $=\frac{1}{2}=m$

Let the point $x=0$

Therefore, the equation is $y=-\frac{9}{2}$

Let the point $x=1$

Therefore, the equation is

  $\begin{array}{l}y=\frac{1}{2}\cdot 1-\frac{9}{2}\\ y=\frac{1}{2}-\frac{9}{2}\\ y=\frac{1-9}{2}\\ y=\frac{-8}{2}\\ y=-4\end{array}$

Therefore, the first and second point are $\left(0,-\frac{9}{2}\right)$ and $\left(1,-4\right)$

Hence, the slope of the line is $\frac{1}{2}$ and the two points are $\left(0,-\frac{9}{2}\right)$ , $\left(1,-4\right)$