Question

graph the inequality y> 1/3 x - 2

Answer 1

To graph y > (1/3)x − 2:

1. Graph the boundary line y = (1/3)x − 2 as a dashed line (because the inequality is strict, >, not ≥).
- y-intercept: (0, −2).
- Use the slope 1/3: from (0, −2) go up 1 and right 3 to get another point (3, −1). Connect these with a dashed line.

2. Decide which side to shade. Test a point not on the line (the origin is easy): plug (0,0) into the inequality:
0 > (1/3)·0 − 2 → 0 > −2, which is true.
So shade the region that contains the origin — i.e., the half-plane above the dashed line.

Result: dashed line y = (1/3)x − 2 and shading of the area above it.