# How do you find the x and y intercepts of 1/2x+2y=-2?

May 7, 2017

See a solution process below:

#### Explanation:

To find the x-intercept:

Substitute $0$ for $y$ and solve for $x$:

$\frac{1}{2} x + 2 y = - 2$ becomes:

$\frac{1}{2} x + \left(2 \cdot 0\right) = - 2$

$\frac{1}{2} x + 0 = - 2$

$\frac{1}{2} x = - 2$

$\textcolor{red}{2} \cdot \frac{1}{2} x = \textcolor{red}{2} \cdot - 2$

$\cancel{\textcolor{red}{2}} \cdot \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} x = - 4$

$x = - 4$

The x-intercept is $x = - 4$ or $\left(- 4 , 0\right)$

To find the y-intercept:

Substitute $0$ for $x$ and solve for $y$:

$\frac{1}{2} x + 2 y = - 2$ becomes:

$\left(\frac{1}{2} \cdot 0\right) + 2 y = - 2$

$0 + 2 y = - 2$

$2 y = - 2$

$\frac{2 y}{\textcolor{red}{2}} = - \frac{2}{\textcolor{red}{2}}$

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

$y = - 1$

The y-intercept is $y = - 1$ or $\left(0 , - 1\right)$