SOLUTION: Graph the inequality on a plane y>6x

Question 145960: Graph the inequality on a plane

y>6x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the 1st inequality

Replace the inequality sign with an equals sign

So in order to plot , we need to plot the equation first

Graph of

Now lets pick a test point, say (0,1). 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 (0,1) into the inequality

Plug in and

Simplify

(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.)

Since this inequality is true, we simply shade the entire region that contains (0,1)

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

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