Question

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
y>2x−2

Answer 1

y < 2x − 2

Reason: the second boundary line in the graph has slope +2 and is dashed (strict inequality). A test point in the shaded region, e.g. (0, −3), satisfies both y ≤ −2x − 1 (−3 ≤ −1) and y < 2x − 2 (−3 < −2), so y < 2x − 2 is the correct partner.