A linear inequality in two variables describes a region on the graph, bounded by a straight line. This section has four lessons and a practice set, and belongs to the SPM Mathematics guide.
What does this section cover?
Start with drawing an inequality boundary correctly, which covers solid and dashed lines. Then learn choosing the shaded side using a test point.
Next is finding a region satisfying several inequalities. The fourth lesson is translating constraints in a word problem, and the practice set mixes all four.
One inequality, three steps
A worked example: show 2x + y ≤ 8.
| Step | Working | Result |
|---|---|---|
| Boundary | Draw 2x + y = 8 through (0, 8) and (4, 0) | Solid, because of ≤ |
| Test point | (0, 0): 2(0) + 0 = 0, and 0 ≤ 8 is true | Shade the side with the origin |
| Check | (5, 5): 15 ≤ 8 is false | (5, 5) lies outside the region |
The same three steps scale up to several inequalities at once.
Who should start where?
If you are unsure which line type to draw, begin with the boundary lesson. If your lines are right but shading goes wrong, start at the test-point lesson.
If single inequalities are comfortable, go to the region lesson and then the word-problem lesson. The line-drawing relies on substituting into equations, which the algebra step repair trainer can refresh.
How do the parts connect?
The boundary depends on the sign, the test point decides the side, and a region is where all the sides overlap. Word problems add one step before the graph: turning sentences into inequalities.
Logging each slip in the mistake log tool shows which step fails most often.
If shading and regions still cost you marks, one-to-one Mathematics tuition lets a teacher check your graphs step by step.