# How do you graph the inequality -2x+y>=-4?

May 30, 2017

Step 1. Dashed or Solid Line

This inequality says that $- 2 x + y$ is greater than or equal to $- 4$. That means that our graph will be a solid line (as opposed to a dashed line).

Step 2. Graph it, pretending it's an equation (not an inequality).

This is easier to solve if you pretend you have a linear equation instead of an inequality. That is, determine what you would graph if you were asked

$- 2 x + y = - 4$

$y = 2 x - 4$

But sure to graph it with a solid line (see Step 1).

graph{2x-4[-2,5,-5,5]}

Step 3. Pick points to decide which side to shade.

Going back to the original inequality, $- 2 x + y \ge - 4$, you should plug in points to see where the inequality is TRUE or FALSE. A good point to pick is always the origin, $\left(0 , 0\right)$.

$- 2 x + y \ge - 4$

$- 2 \left(0\right) + 0 \ge - 4$

$0 \ge - 4$ is TRUE, so shade on the side of the line containing the point $\left(0 , 0\right)$. The graph looks like this.

graph{(y-2x+4)>=0[-2,5,-5,5]}