# How do you find the x and y intercepts of  2x-3y= -12?

Feb 22, 2017

See the entire solution process below:

#### Explanation:

To find the x-intercept by substitution set $y = 0$ and solve for $x$:

$2 x - \left(3 \times 0\right) = - 12$

$2 x - 0 = - 12$

$2 x = - 12$

$\frac{2 x}{\textcolor{red}{2}} = - \frac{12}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = - 6$

$x = - 6$ for $y = 0$ therefore the x-intercept is $- 6$ or $\left(- 6 , 0\right)$

To find the y-intercept by substitution set $x = 0$ and solve for $y$:

$\left(2 \times 0\right) - 3 y = - 12$

$0 - 3 y = - 12$

$- 3 y = - 12$

$\frac{- 3 y}{\textcolor{red}{- 3}} = \frac{- 12}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} y}{\cancel{\textcolor{red}{- 3}}} = 4$

$y = 4$ for $x = 0$ therefore the y-intercept is $4$ or $\left(0 , 4\right)$