Linear Inequalities in Two Variables · 6.1.3
Shading the region of an inequality
Pupils draw the boundary line of a linear inequality on a Cartesian plane, using a solid line when the inequality includes equality and a dashed line when it is strict. They then shade the side of the line containing all points that satisfy the inequality, checked using a test point.
The official learning standard (6.1.3)
“Determine and shade the region that satisfies a linear inequality.”
What it means
Pupils draw the boundary line of a linear inequality on a Cartesian plane, using a solid line when the inequality includes equality and a dashed line when it is strict. They then shade the side of the line containing all points that satisfy the inequality, checked using a test point.
How it is examined
Paper 2 questions require pupils to draw axes, plot a straight line from its equation with the correct line type, and shade the correct region for a given inequality. Marks are awarded for an accurate line, correct line style, and correctly shaded region matching the inequality symbol given.
Worked example
On a Cartesian plane, draw and shade the region that satisfies the inequality y < 2x + 1.
- Draw the line y = 2x + 1 using two points, such as (0, 1) and (2, 5).
- Since the inequality is strict (<), draw the line as dashed to show points on it are excluded.
- Test a point not on the line, such as (0, 0): 0 < 2(0) + 1 = 1, which is true.
- Since (0, 0) satisfies the inequality, shade the region containing (0, 0), i.e. below the line.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I decide between a solid and a dashed line?
Use a solid line when the inequality includes "equal to", such as ≤ or ≥, meaning points on the boundary are part of the solution. Use a dashed line for strict inequalities, such as < or >, meaning the boundary line itself is excluded from the solution.
Which side of the line should I shade?
Pick any point not on the line, usually (0, 0) if it is not on the line, and substitute its coordinates into the inequality. If the resulting statement is true, shade the side containing that point; if false, shade the opposite side instead.
What if the line passes through the origin?
Choose a different test point instead, such as (1, 0) or (0, 1), since substituting (0, 0) would give a result of zero on both sides and would not help decide the correct side to shade.