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
y > x – 2 and x + 2y < –4

Answer 1

The first line through (0, −2) and (2, 0) is y = x − 2. The shaded side is the region above/left of it, so y > x − 2.
The second line through (0, 2) and (4, 0) is x + 2y = 4 and it is dashed; the shaded side contains (0,0), so x + 2y < 4.

Answer: y > x − 2 and x + 2y < 4.