Chapter 13.7, Problem 8WE

To determine

To find : an equation of line described

Answer to Problem 8WE

The equation of the line is $y=\frac{1}{3}x-3$

Explanation of Solution

Given information :

The line is

  $x$ -intercept $=9$ ; $y$ -intercept $=-3$

Formula used :

  $y=mx+b$

Calculation :

The equation of the line is

Because $y$ -intercept is $-3$ , so $b=-3$ .

Because the point $\left(9,0\right)$ and $\left(0,-3\right)$ lie on the line,

Slope $=\frac{-3-0}{0-9}=\frac{-3}{-9}=\frac{1}{3}$ .

Since the slope is $\frac{1}{3}$ , so $m=\frac{1}{3}$ .

Now substitute into the equation $y=mx+b$ to get

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

Hence, the equation of the line is $y=\frac{1}{3}x-3$ .