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
y>2x−2

Answer 1

The second line through (0,2) and (1,0) has slope -2, so its equation is y = -2x + 2. It's dashed (strict) and the right side is shaded — test point (2,0): 0 > -2(2)+2 = -2, so the inequality is y > -2x + 2.

So the system is y ≤ -2x - 1 and y > -2x + 2.