Question

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

Answer 1

Step 1. Dashed or Solid Line

This inequality says that `-2x+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

`-2x+y=-4`

`y=2x-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, `-2x+y>=-4`, you should plug in points to see where the inequality is TRUE or FALSE. A good point to pick is always the origin, `(0,0)`.

`-2x+y>=-4`

`-2(0)+0>=-4`

`0>=-4` is TRUE, so shade on the side of the line containing the point `(0,0)`. The graph looks like this.

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