Question

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 1) and (0, 1). Everything to the left of the line is shaded.

Answer 1

First find the line through (-1,-1) and (0,1). Slope m = (1 - (-1))/(0 - (-1)) = 2, so the line is y = 2x + 1.

The line is dashed, so the inequality is strict. To decide > or <, test a point that lies on the shaded (left) side; for example (-2,0) is on the left. Check: 0 ? 2(-2)+1 → 0 ? -3, so 0 > -3. Thus the shaded region satisfies

y > 2x + 1.

(Equivalently 2x - y < -1.)