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

1 Answer
Jo S.
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=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.

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