Question

On a coordinate plane, 2 dashed lines are shown. The first straight line has a negative slope and goes through (0, 1) and (2, 0). Everything below and to the left of the line is shaded. The second straight line has a positive slope and goes through (negative 1, 0) and (0, 2). Everything above and to the left of the line is shaded. A point is shown at (negative 3, 1).
Which system of inequalities with a solution point is represented by the graph?

y > 2x – 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x – 2 and y < Negative one-halfx + 1; (–3, 1)
y > 2x + 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x + 2 and y < Negative one-halfx + 1; (–3, 1)

Answer 1

y > 2x + 2 and y < −(1/2)x + 1; (−3, 1)

Explanation: The positive-slope line through (−1,0) and (0,2) is y = 2x + 2 and is shaded above → y > 2x + 2. The negative-slope line through (0,1) and (2,0) is y = −(1/2)x + 1 and is shaded below → y < −(1/2)x + 1. The point (−3,1) satisfies both.