what is the easiest way to graph inequality

Question

I am kind of curious because this is the hardest thing on the mid-term review we have to do

 

Answer 1

Makayla, I'll give you an example.

 

5x - 5y < 15

 

First, let's get it into something we can graph.

 

-5y < -5x + 15

   y > x - 3

 

Notice, the sign switched at the end. Dividing by a negative number turns the sign around.

 

Now, we have the y-intercept at -3 and a slope of 1. Because we do not have a "or equal to" we draw a dotted line.

 

We then shade everything above the dotted line.

 

Let's check. (0,1) should fall in our shaded area.

 

5(0) - 5(1) < 15

          0 - 5 < 15

               -5 < 15

 

This is true!

 

We can also pick a point on the line. Let's use the y-intercept, (0,-3).

 

5(0) - 5(-3) < 15

         0 +15 < 15

               15 < 15

 

This is NOT true, which is why we used a dotted line.

 

Make sense?