Chapter 13.7, Problem 10WE

To determine

To find : an equation of line described

Answer to Problem 10WE

The equation of the line is $y=\frac{-2}{5}x-2$

Explanation of Solution

Given information :

The line is

  $x$ -intercept $=-5$ ; $y$ -intercept $=-2$

Formula used :

  $y=mx+b$

Calculation :

The equation of the line is

Because $y$ -intercept is $-2$ , so $b=-2$ .

Because the point $\left(-5,0\right)$ and $\left(0,-2\right)$ lie on the line,

Slope $=\frac{-2-0}{0-\left(-5\right)}=\frac{-2}{5}$ .

Since the slope is $\frac{-2}{5}$ , so $m=\frac{-2}{5}$ .

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

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

Hence, the equation of the line is $y=\frac{-2}{5}x-2$ .