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.

EnglishLinear inequality
Bahasa MelayuKetaksamaan 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

Linear equationA linear equation like y = 2x + 1 gives a single line; a linear inequality like y ≥ 2x + 1 gives a whole region of the plane.
Quadratic inequalityA linear inequality has variables to power 1 with a straight boundary; a quadratic inequality involves x² and a curved boundary.

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.

Related terms

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