Question

On a coordinate plane, 2 solid straight lines are shown. The first line has a negative slope and goes through (negative 4, negative 2) and (0, negative 3). Everything above the line is shaded. The second line has a positive slope and goes through (0, negative 2) and (2, 2). Everything above the line is shaded.
Which number completes the system of linear inequalities represented by the graph?

y > 2x – 2 and x + 4y >

Answer 1

First line through (-4,-2) and (0,-3): slope = (-3 - (-2))/(0 - (-4)) = -1/4, so y = (-1/4)x - 3. Multiply by 4: x + 4y = -12. Since the region above the line is shaded, x + 4y > -12.

Answer: -12.