Question

Which linear inequality is represented by the graph?

y > Two-thirdsx – One-fifth
y ≥ Three-halvesx + One-fifth
y ≤ Two-thirdsx + One-fifth
y < Three-halvesx – One-fifth

Answer 1

I don't see the graph — could you upload it or describe it? To pick the correct inequality, check three things on the graph:

1. y‑intercept (where the line crosses the y‑axis): is it +1/5 or −1/5?
2. Slope (steepness): is the line gently rising (slope = 2/3) or steeply rising (slope = 3/2)?
3. Line style and shading: is the boundary solid (includes =) or dashed (strict > or <)? Is the shaded region above the line (use > or ≥) or below the line (use < or ≤)?

Quick mapping of the choices:
- y > (2/3)x − 1/5 : dashed line, slope 2/3, intercept −1/5, shading above.
- y ≥ (3/2)x + 1/5 : solid line, slope 3/2, intercept +1/5, shading above.
- y ≤ (2/3)x + 1/5 : solid line, slope 2/3, intercept +1/5, shading below.
- y < (3/2)x − 1/5 : dashed line, slope 3/2, intercept −1/5, shading below.

Tell me the y‑intercept, whether the line is solid or dashed, and whether the shaded side is above or below, and I’ll pick the exact inequality.