Graphing linear inequalities is covered in high school math.

Let’s imagine you need to graph the inequality

2x-3y≤12

I recommend that to start, you graph the corresponding equation

2x-3y=12

which will be a line. (See my post here about how to graph a line.)

To graph 2x-3y=12, we might start with a table of values in which we set first x to 0, then y:

To find y when x=0, we substitute 0 in for x and solve:

2(0)-3y=12

-3y=12

Dividing both sides by -3 gives

y=-4

Next, we find x when y=0:

2x-3(0)=12

2x=12

Dividing both sides by 2 gives

x=6

We can complete our table now:

Next, we plot the two points from the table, (0,-4) and (6,0), on a graph and draw a line through them:

We have graphed the equation 2x-3y=12. To graph the inequality 2x-3y≤12, we will need to shade on one side of the line. To determine which side, we use a test point, which is a point not on our line. When we can, we like to use (0,0). In this case, we can use (0,0), since it’s not on the line we’ve drawn.

We plug our test point, which is in this case (0,0), into 2x-3y≤12:

2(0)-3(0)≤12

which gives

0≤12

Since the statement 0≤12 is true, we shade the side (0,0) is on:

Points to note about graphing inequalities in general:

1) If the test point makes your inequality false, you shade the other side of the line, not the side on which the test point is found.

2) If your line passes through (0,0), you must choose another test point instead. Perhaps you could use (0,1) or (1,0) in such a case.

3) If the inequality is a strict inequality (that is, it uses < or > rather than ≤ or ≥), you use a dotted line rather than a solid line.

While there are still more points to raise about this topic, the content here is a good primer. I’ll continue with linear inequalities and their graphs in future posts.

HTH:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.