We started our inequalities unit this week. If you were told how to graph , I’m sure you’d be able to graph it. Or y=2x-3? What if I asked you to graph How do you graph that?

First, lets refresh what inequality signs mean. The means “greater than or equal to”. For example, or . While the means “less than or equal to”. For example, or .

Now that we’ve got that out of the way, now we learn how to graph  an inequality. It’s just like graphing a linear equation, just with an extra step. In , we can see that the inequality is in our slope-intercept form, which you probably learned back in grade 9. Our slope here is 2, and our y-intercept is 3. Make your starting point on the graph your y-intercept, and then draw your slope.

To show our inequality, we highlight the side of the graph, where if we use a point from that highlighted side, the inequality statement will be true.

Okay, okay, that was a mouthful. Just, keep with me, here.

Our last step involves using a “test point”. Now that we’ve graphed our line, we’ve split the graph into two parts. Pick a point that is clearly on one side of the line, say, (-5, -5). Insert the coordinates into your inequality.

 

 

 

If the statement is true, then that means for the inequality statement to be true, you have to insert the coordinates for any point that is on that side. If you got a false statement, that means that the other side is correct! Then you just highlight the correct side.