Question

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

Answer 1

See step below in the explanation: you would plot `y=-1/2x-2` and shade the area where `y > -1/2x-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:
`-2x-4y<=8 -> 4y>=-2x-8 -> y>=-1/2x-2`

2) Plot the `y=-1/2x-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]}