# How do you graph the inequality -2x - 4y ≤ 8?

May 23, 2018

See step below in the explanation: you would plot $y = - \frac{1}{2} x - 2$ and shade the area where $y > - \frac{1}{2} x - 2$

#### Explanation:

What we will do, is first, graph the "equals" line, then shade in the correct area.

There are three steps to do this:

1) Rearrange the equation so "y" is on the left and everything else on the right.
2) Plot the "y=" line
3) Shade above the line for a "greater than" (y≥).

In our instance:
1) Rearrange the equation so "y" is on the left:
$- 2 x - 4 y \le 8 \to 4 y \ge - 2 x - 8 \to y \ge - \frac{1}{2} x - 2$

2) Plot the $y = - \frac{1}{2} x - 2$ line:

graph{y=-1/2x-2 [-7.9, 7.9, -3.95, 3.95]}

3) Shade above the line for a "greater than" (y≥):

graph{y>=-1/2x-2 [-7.89, 7.91, -3.95, 3.95]}