Algebra
Graphing inequalities
Shade the half-plane below or above — and the boundary line tells you which.
On a number line: open circle for strict (<, >), filled circle for inclusive (≤, ≥). On a plane: shade the half above or below the boundary line.
Drag the sliders
y = m·x + b
Turning a line into a region
- Graph the boundary line y = mx + b (this widget shows it).
- Dashed line for strict < or > (boundary not included); solid for ≤ or ≥.
- Shade above the line for y > / y ≥; below for y < / y ≤.
- Unsure which side? Test (0, 0): if it satisfies the inequality, shade that side.
Your turn
Describe the graph of y ≤ −x + 3.
On a one-variable number line instead: open circle for < or >, filled circle for ≤ or ≥, arrow pointing toward the solutions.
Try it
Graph y > 2x + 1
Dashed line y = 2x + 1, shade above.