Chapter 13.7, Problem 19WE

To determine

To find : an equation of line described

Answer to Problem 19WE

The equation is $y=\frac{1}{3}x+2$

Explanation of Solution

Given information :

Line through $\left(-3,1\right)$ and $\left(3,3\right)$

Formula used :

  $m=\frac{y-y_1}{x-x_1}$

Calculation :

To find the slope

  $\begin{array}{l}m=\frac{1-3}{-3-3}\\ m=\frac{-2}{-6}\\ m=\frac{1}{3}\end{array}$

Then use the point and slope

Using $\left(-3,1\right)$ , the equation is

  $\begin{array}{l}y-1=\frac{1}{3}\left(x-\left(-3\right)\right)\\ y=\frac{1}{3}x+\frac{3}{3}+1\\ y=\frac{1}{3}x+1+1\\ y=\frac{1}{3}x+2\end{array}$

Using $\left(3,3\right)$ , the equation is

  $\begin{array}{l}y-3=\frac{1}{3}\left(x-3\right)\\ y=\frac{1}{3}x-\frac{3}{3}+3\\ y=\frac{1}{3}x-1+3\\ y=\frac{1}{3}x+2\end{array}$

Hence, the equation is $y=\frac{1}{3}x+2$ .