Question

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

$6x=-12y+48$

Short answer

The x-intercept is $8$.

The y-intercept is $4$.

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:

$6x=-12y+48$

Putting $y=0$:

$\begin{array}{c}6x=-12\left(0\right)+48\\ 6x=48\\ x=8\end{array}$

Hence, x-intercept is 8.

– Determining the y-intercept

We have:

$6x=-12y+48$

Putting $x=0$:

$\begin{array}{c}6\left(0\right)=-12y+48\\ 0=-12y+48\\ 12y=48\\ y=4\end{array}$

Hence, y-intercept is 4.