Question

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?

y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2

Answer 1

Slope = (2 - (-7)) / (0 - (-3)) = 9/3 = 3, and y-intercept is 2, so the line is y = 3x + 2. The line is dashed so the inequality is strict. Using a test point in the shaded region (for example (0,0)): 0 < 3(0)+2 = 2, so the shaded side satisfies y < 3x + 2.