Linear Inequalities in Two Variables
Linear inequality
A relationship like y ≥ 2x + 1 that describes a region of the graph rather than a single line.
| English | Linear inequality |
|---|---|
| Bahasa Melayu | Ketaksamaan linear |
| 中文 | 线性不等式 |
How it is used
The inequality y ≥ 2x + 1 is a linear inequality: the line y = 2x + 1 is drawn solid, and the region on and above it (for example the point (0, 3), since 3 ≥ 1) is shaded.
Where it shows up in SPM
Central to Form 5 Linear Inequalities in Two Variables. In Paper 2 you shade the region of one or several inequalities on a grid; in Paper 1 objective items you match an inequality to a shaded region or pick the correct sign (solid vs dashed boundary).
Don't confuse it with
Open the chapter: Linear Inequalities in Two Variables →
Frequently asked questions
When do I draw the boundary solid and when dashed?
Use a solid line for ≤ or ≥, because points on the line are included. Use a dashed line for < or >, because the line itself is not part of the region.
For y > 2x + 1 the boundary is dashed; for y ≥ 2x + 1 it is solid.
Which side of the line do I shade?
Pick a test point not on the line, usually (0, 0), and put it into the inequality. If it makes the inequality true, shade that side; if false, shade the other side.
For y ≥ 2x + 1, (0, 0) gives 0 ≥ 1 which is false, so shade the side away from the origin.