SOLUTION: solve and graph the following inequality 3x-4y<12

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Question 87378: solve and graph the following inequality
3x-4y<12
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

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, but this point is the easiest to work with), and evaluate the inequality

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)
(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)