Question

On a coordinate plane, 2 dashed straight lines are shown. The first line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything to the right of the line is shaded. The second line has a negative slope and goes through (negative 2, 0) and (2, negative 4). Everything to the right of the line is shaded.
Which linear inequality is graphed with y > –x – 2 to create the given solution set?

y > x + 1
y < x – 1
y > x – 1
y < x + 1

Answer 1

The first line through (-1,0) and (0,1) has equation y = x + 1. For a line with positive slope, "to the right" is the half-plane below the line, so the inequality is y < x + 1. Thus the correct choice is y < x + 1.