Question

Find the x-intercept and the y-intercept of the graph of each equation. Then graph the equation.

$-\frac{1}{5}y=x+4$

Short answer

The x-intercept is $-4$.

The y-intercept is $\frac{21}{5}$.

Step-by-step solution

– Defining the x-intercept and y-intercept

The x-intercept is the value of x when $y=0$.

The y-intercept is the value of y when $x=0$.

– Determining the x-intercept

We have:

$-\frac{1}{5}y=x+4$

Putting $y=0$:

$\begin{array}{c}-\frac{1}{5}\left(0\right)=x+4\\ 0=x+4\\ x=-4\end{array}$

Hence, x-intercept is $-4$.

– Determining the y-intercept

We have:

$-\frac{1}{5}y=x+4$

Putting $x=0$:

$\begin{array}{c}-\frac{1}{5}y=0+4\\ y=\frac{1}{5}+4\\ y=\frac{21}{5}\end{array}$

Hence, y-intercept is $\frac{21}{5}$.