Jack M. answered • 12/02/12

Keys to Chemistry, Calculus, Literature and More

Hello, Valerie --

First you need to find the x-intercept and the y-intercept. Divide all the way through by 3 to reduce the inequality to an equivalent form:

2x + y > 6

To find the y-intercept, let x = 0, and change > to =:

2(0) + y = 6

**y-intercept is (0,6)**

For the x-intercept, let y = 0:

2x + (0) = 6

**x-intercept is (3,0)**

Put those points on your graph and draw a dotted line through them (dotted because of the > inequality).

To finish the graph shade either above or below the dotted line. To determine the shaded area, pick a "test point" -- say (0,0) -- and substitute those values into the original. See whethere the result is true or false.

6(0) + 3(0) > 9

This is false, because 0 < 9. You know now that the point (0,0) is NOT in the shaded area. It is below the dotted line, your shading must be above the line.

You could check another point -- say (3,2) to make sure. That point is above the line,making the inequality true, so it will be in the shaded area.