Question

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.
Which system of linear inequalities is represented by the graph?

y > x – 2 and x – 2y < 4
y > x + 2 and x + 2y < 4
y > x – 2 and x + 2y < 4

Answer 1

First line through (0,-2) and (2,0) has slope 1 so its equation is y = x − 2. “Left” of that slanted line is the region above it, so y > x − 2 (solid line would allow ≥, but the choices use >).

Second line through (0,2) and (4,0) has equation y = −(1/2)x + 2, or x + 2y = 4. “Below and to the left” of this dashed line contains (0,0), so the half-plane is x + 2y < 4.

Thus the correct system is: y > x − 2 and x + 2y < 4 (option 3).