SOLUTION: When graphing a linear inequality, how do you know if the inequality represents the area above the line?

Question 246020: When graphing a linear inequality, how do you know if the inequality represents the area above the line?
Answer by marcsam823(57) (Show Source): You can put this solution on YOUR website!
Let's use the inequality y > 2x + 4 as an example.
Graph the line y = 2x + 4 (just pick any two values for x, solve each for y and draw a line between the two points; I'll use 0,4 and 1,6)
Pick a test point on either side of the line and plug it into the inequality. If the test point makes the inequality y > 2x + 4 true then all points on that side of the line will make the inequality true. Similarly, if the point makes the inequality false then all points on the same side of the line will make the inequality false.
Note: in this case, the points ON the line are not part of the solution

Let's use the origin (0,0) as the sample point.
Substitute:

This inequality is false so all points "under" the line would make the inequality false as well (test it for yourself using other points), so the solution to the inequality would be all points above the line not including the points on the line itself.
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