# How do you find the x and y intercept of -3x+9y=-18?

May 17, 2017

The $x$-intercept is $\left(6 , 0\right)$
The $y$-intercept is $\left(0 , - 2\right)$

#### Explanation:

The $x$-intercept occurs when $y$ equals zero, and the $y$-intercept is when $x$ equals zero.

Knowing that, let's solve for our $x$-intercept by setting $y = 0$.

$- 3 \times x + 9 \times 0 = - 18$

$- 3 \times x = - 18$

divide by $- 3$

$x = 6$

The $x$-intercept is $\left(6 , 0\right)$

Now let's solve for the $y$-intercept

$- 3 \times 0 + 9 \times y = - 18$

$9 \times y = - 18$

divide by $9$ on both sides

$x = - 2$

The $y$-intercept is $\left(0 , - 2\right)$

Just to check our work, let's graph the equation and see if our $x$ and $y$ intercepts match:

graph{-18=-3x+9y}

They match! Good job!