Question

How do you graph `9x-9y> -36` on the coordinate plane?

Answer 1

The half plane above and to the left of `y=x+4`.

Explanation:

Simplify first, to give `x-y> -4` then temporarily convert it to an equation so we can draw the critical line: `x-y=-4`.
If you like to use the `y=mx+c` format, you can rearrange your equation to `y=x+4`.
Depending on the requirement of the curriculum you're following, you might draw the line dotted to indicate strict inequality (the editor here does not allow this):
graph{x+4 [-9.125, 10.875, -2.24, 7.76]}
Next you need to decide which side of the line agrees with the inequality. I like to use `(0, 0)` as a test (as long as it doesn't sit on the line).
Is it true that `9xx0-9xx0< -36`?
It is not true, therefore the half of the plane split by the critical line which contains the point `(0, 0)` does not satisfy the inequality.
The correct half of the plane is the part above and to the left of the critical line.