Question

The solid line starts at the coordinates left parenthesis negative 6 comma negative 10 right parenthesis. It has an x-intercept at negative 1, a y-intercept at two, and ends at the coordinates left parenthesis 4 comma 10 right parenthesis.
Which linear inequality matches the given graph?
(1 point)
y > 2x + 2
y < 2x + 2
y ≤ 2x + 2
У ≥ 2x + 2

Answer 1

First find the line. Using the x‑intercept (−1,0) and y‑intercept (0,2) gives slope 2, so the equation is y = 2x + 2.

The line is solid, so the inequality includes equality (≤ or ≥), not < or >. To choose ≤ versus ≥, test a point not on the line (for example (0,0)):

- If the shaded region contains (0,0), then 0 ≤ 2 is true, so the inequality is y ≤ 2x + 2.
- If the shaded region is the area above the line (does not contain (0,0)), then the inequality is y ≥ 2x + 2.

Tell me whether the region shaded is above or below the line (or whether (0,0) is shaded), and I’ll pick the correct choice.