Question

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 2, 3) and (0, negative 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (1, 0). Everything to the right of the line is shaded.
Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph?

y<−2x+2
y>−2x+2
y<2x−2

Answer 1

The dashed line through (0,2) and (1,0) has slope −2, so its equation is y = −2x + 2. It's dashed (strict inequality). A point to the right of the line (e.g. (2,0)) gives 0 > −4, so the shaded side satisfies y > −2x + 2.

Thus the system is
y ≤ −2x − 1
y > −2x + 2.