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

Answer 1

Steps to graph y ≥ −(1/3)x − 6

1. Identify the boundary line: y = −(1/3)x − 6.
- y‑intercept: (0, −6). Plot this point.
- x‑intercept: set y=0 → −(1/3)x − 6 = 0 → x = −18. Plot (−18, 0).
- Slope: −1/3 means rise −1 for run +3. From (0, −6) go right 3 and down 1 to (3, −7), or left 3 and up 1 to (−3, −5). Plot a second point and draw the line through the points.

2. Use a solid line for the boundary because the inequality is “greater than or equal to” (≥).

3. Shade the region “above” the line (the side where y values are larger).
- Quick check: test (0,0). Substitute: 0 ≥ −6 is true, so shade the side containing (0,0).

Result: the solid line y = −(1/3)x − 6 with the region above it shaded (including the line).