# How do you find the x and y intercepts of -6x+8y=-36?

Apr 4, 2017

See the entire solution process below:

#### Explanation:

To find the y-intercept, set $x$ to $0$ and solve for $y$:

$\left(- 6 \times 0\right) + 8 y = - 36$

$0 + 8 y = - 36$

$8 y = - 36$

$\frac{8 y}{\textcolor{red}{8}} = - \frac{36}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} y}{\cancel{\textcolor{red}{8}}} = \frac{4 \times - 9}{\textcolor{red}{4 \times 2}}$

$y = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times - 9}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{4}}} \times 2}}$

$y = - \frac{9}{2}$

The y-intercept is $- \frac{9}{2}$ or $\left(0 , - \frac{9}{2}\right)$

To find the x-intercept, set $y$ to $0$ and solve for $x$:

$- 6 x + \left(8 \times 0\right) = - 36$

$- 6 x + 0 = - 36$

$- 6 x = - 36$

$\frac{- 6 x}{\textcolor{red}{- 6}} = \frac{- 36}{\textcolor{red}{- 6}}$

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

$x = 6$

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