Question

Graph the inequality on the axes below.
y, is greater than or equal to, minus, one third, x, minus, 6
y≥−1/3x−6 on a graph with two points

Answer 1

To graph y ≥ −(1/3)x − 6:

1. Find two points on the boundary line y = −(1/3)x − 6. For example:
- x = 0 → y = −6 → (0, −6)
- x = 3 → y = −1 − 6 = −7 → (3, −7)
(Alternatively x = −3 → y = 1 − 6 = −5 → (−3, −5).)

2. Plot those two points and draw a solid straight line through them (solid because the inequality is ≥, so points on the line are included).

3. Shade the region above the line (the side with larger y). To check which side: test (0,0). Since 0 ≥ −6 is true, shade the side containing (0,0).

That completes the graph: a solid line through (0, −6) and (3, −7), shading the region above it.