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

Oct 30, 2017

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 $y = m x + c$ 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 $\left(0 , 0\right)$ as a test (as long as it doesn't sit on the line).
Is it true that $9 \times 0 - 9 \times 0 < - 36$?
It is not true, therefore the half of the plane split by the critical line which contains the point $\left(0 , 0\right)$ does not satisfy the inequality.
The correct half of the plane is the part above and to the left of the critical line.