SOLUTION: Graph 8x-7<=15+y

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Question 193079: Graph 8x-7<=15+y
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given inequality

Subtract y from both sides.

Add 7 to both sides.

Combine like terms.

Now let's graph

In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver )

graph of

Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point

Substitute (0,0) into the inequality

Plug in and

Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0)

Graph of with the boundary (which is the line in red) and the shaded region (in green)