At GCSE you have to be able to illustrate inequalities. When you have a single variable inequality (such as 2x + 1 > 7) you can do this with a number line. However, what do we do when we have inequalities that contain two variables.
We use a set of axes.
The difference between greater than and greater than or equal to.
When we draw inequalities on a number line, we use a shaded circle for greater than or equal to and an unshaded on for greater than.
When we are drawing on a set of axes, we have to change this slightly.
Greater Than/Less than – We use a dashed line
Greater Than or Equal to/Less than or equal to – We use a solid line.
Example 1: Draw the inequality y > 3x + 1
The first step here is to work out if we need a solid or a dashed line. As the inequality is a greater then, we use a dashed line.
The next step is to work out the line. To do this, we ignore the inequality and draw the line y = 3x + 1
Once we have drawn the line, we need to decide which side to shade to illustrate the inequality. To do this, we pick a point (I think 0,0 is the best one), plug this into the inequality and see if the point satisfies the inequality.
We know at (0,0), x = 0 and y = 0
Y > 3x + 1
0 > 3(0) + 1
0 > 1
We can see very clearly that this isn’t true, so we shade above the line (if it was true, we would shade below)
Example 2: Draw the inequality 5x + 2y ≤ 10
Once again, we pick our line type first. As this is less than or equal to, we use a solid line.
Once again, we need to test to see which side we need to shade. I’m going to use (0,0) again.
5x + 2y ≤ 10
5(0)+ 2(0) ≤ 10
0 ≤ 10
Because this is true, we know that this is the side of the line we need to shade.
Example 3: Draw the inequality -2 < x ≤ 1
It is really common with this style of questions that you have to draw single variable inequalities on a set of axes. To do this, we have to look at the inequality as two lines. -2 < x and x ≤ 1.
If we draw this on a set of axes, we get…
We don’t need to test this one as the inequality is quite clear. We are looking for the points between -2 and 1 so our shading would look like…