The Region Shader
Foundation Tier • Section 2.8D • Linear Inequalities (Regions)
Logic Track
Solid vs Dashed Lines
Strict inequality ($<$ or $>$) uses a DASHED line (the fence is electric - you can't touch it).
Inclusive inequality ($\le$ or $\ge$) uses a SOLID line (you can touch the fence).
The Test Point Method
For inequality $y \le x + 2$, test point (0, 0):
0 ≤ 0 + 2 → 0 ≤ 2 ✓ TRUE
Since (0,0) satisfies the inequality, shade the region containing (0,0).
Region Checker (Dynamic Solver)
Test if point is inside region: 2x + y < 6
Step-by-Step Working:
Inequality: 2x + y < 6
Substitute: 2(2) + 1 = 5
Check: 5 < 6
✓ Point is INSIDE the region