Question

On a coordinate plane, a solid straight line has a positive slope and goes through (0, 0.2) and (3, 2.2). Everything to the right of the line is shaded.
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

Slope = (2.2 − 0.2)/(3 − 0) = 2/3 and y-intercept = 0.2 = 1/5, so the line is y = (2/3)x + 1/5. A solid line with the region "to the right" of a positively sloped line is the half-plane below it, so the inequality is y ≤ (2/3)x + 1/5.