Question

Which linear inequality is represented by the graph?

y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1

Answer 1

I can’t see the graph. Could you upload it or describe it (whether the boundary line is solid or dashed, a point or two on the line, and which side is shaded)?

How to decide (quick steps):
1. Identify the boundary line from two points on it to get slope and intercept. If it goes through (0, −1) and (3, 0) the slope is 1/3; if it goes through (0, −1) and (1, 2) the slope is 3.
2. Check whether the boundary line is solid (includes the line → ≤ or ≥) or dashed (does not include the line → < or >).
3. Pick a test point not on the line (often (0,0)). If that point is in the shaded region, plug it into the candidate inequalities:
- If (0,0) is shaded: 0 ≤ 1/3·0 −1 is false, 0 ≥ 1/3·0 −1 is true; 0 < 3·0 −1 is false, 0 > 3·0 −1 is true. So that distinguishes which slope and which inequality sign.

Give the graph or that description and I’ll pick the correct choice for you.