Question

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?

y < Two-thirdsx + 3
y > Three-halvesx + 3
y > Two-thirdsx + 3
y < Three-halvesx + 3

Answer 1

Find the slope: m = (3 − 1)/(0 − (−3)) = 2/3, so the line is y = (2/3)x + 3. The line is dashed, so the inequality is strict. Pick a point on the left side (e.g. (−3,3)). For x = −3, (2/3)(−3)+3 = 1, and 3 > 1, so points left of the line satisfy y > (2/3)x + 3.

Answer: y > Two‑thirds x + 3.