Question

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded.

Which linear inequality is represented by the graph?

y ≤ One-halfx + 2
y ≥ One-halfx + 2
y ≤ One-thirdx + 2
y ≥ One-thirdx + 2

Answer 1

Slope = (2 - 0)/(0 - (-4)) = 1/2, so the line is y = (1/2)x + 2. It's solid, so ≤ or ≥. "Right of the line" (for a positively sloped line) is the region below it. Test a point to the right, e.g. (4,0): 0 ≤ (1/2)(4) + 2 = 4 is true. Thus the inequality is y ≤ (1/2)x + 2.