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

Find the line: slope = (2−0)/(0−(−4)) = 2/4 = 1/2, so the equation is y = (1/2)x + 2 and the line is solid.

Pick a test point on the shaded (right) side, e.g. (4,0). Plug into y ? (1/2)x + 2: 0 ≤ (1/2)(4) + 2 = 4, true. So the shaded side satisfies y ≤ (1/2)x + 2.

Answer: y ≤ One-half x + 2.