Plotting an inequality
Treat the inequality as an equation, plot the line, decide solid vs dashed, then shade.
Method.
- Replace the inequality sign with to get a boundary line.
- Plot the line:
- Dashed if STRICT ( or ).
- Solid if INCLUSIVE ( or ).
- Test a point NOT on the line (the origin if possible). If it satisfies the inequality, shade THAT side. Otherwise shade the OPPOSITE side.
Worked. Plot .
- Boundary: . Solid line.
- Test origin : ? No. So shade the side AWAY from the origin (the upper side).
Worked. Plot .
- Boundary: . Dashed.
- Test origin: ? Yes. Shade the side CONTAINING the origin (lower-left).
Cambridge usually wants you to shade the region that satisfies the inequality (the WANTED region). Some textbooks shade the UNWANTED region — read the question carefully.
- Replace with to draw the line.
- Solid for . Dashed for .
- Test a point off the line.
- Shade the side satisfying the inequality (default Cambridge convention).