Jeremy's Math Blog: Unit 5: Day 4

Today, Students will learn to graph linear inequalities.
First off, let me say that graphing linear inequalites is much easier than your book makes it look. Here's how it works:
Think about how you've done linear inequalities on the number line. For instance, they'd ask you to graph something like x > 2. How did you do it? You would draw your number line, find the "equals" part (in this case, x = 2), mark this point with the appropriate notation (an open dot or a parenthesis, indicating that the point x = 2 wasn't included in the solution), and then you'd shade everything to the right, because "greater than" meant "everything off to the right". The steps for graphing two-variable linear inequalities are very much the same.

Graph the solution to 2x – 3y < 6.

First, I'll solve for y:

2x – 3y < 6

–3y < –2x + 6

y > (²/₃ )x – 2

[Note the flipped inequality sign in the last line. I mustn't forget to flip the inequality if I multiply or divide through by a negative!] Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved
Now I need to find the "equals" part, which is the line y = (²/₃ )x – 2. It looks like this:

But this exercise is what is called a "strict" inequality. That is, it isn't an "or equals to" inequality; it's only "y greater than". When I had strict inequalities on the number line (such as x< 3), I denote this by using a parenthesis (instead of a square bracket) or an open [unfilled] dot (instead of a closed [filled] dot). In the case of these linear inequalities, the notation for a strict inequality is a dashed line. So the border of my solution region actually looks like this:

By using a dashed line, I still know where the border is, but I also know that the border isn't included in the solution. Since this is a "y greater than" inequality, I want to shade above the line, so my solution looks like this: