SOLUTION: help please: -12x+8y<56 Graph each linear inequality. (please show steps)

Question 161963: help please: -12x+8y<56 Graph each linear inequality. (please show steps)
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

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). In other words, we shade the entire region that is below 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)

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