SOLUTION: how would i graph this inequality y-4

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Question 189697This question is from textbook Algebra 1
: how would i graph this inequality
y-4 < x-6 This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given inequality

Add 4 to both sides.

Combine like terms.

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 NOT true, we do NOT shade the entire region that contains (0,0). So this means we shade the entire region that is on the opposite side of the line

Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)

SOLUTION: how would i graph this inequality y-4 < x-6