Question

On a coordinate plane, a dashed straight line with positive slope goes through (0, 0.75) and (2, 4.75). Everything to the left of the line is shaded.
Which inequality is represented by the graph?


Which point is a solution to the inequality?

Answer 1

The line through (0, 0.75) and (2, 4.75) has slope (4.75−0.75)/2 = 2, so its equation is y = 2x + 0.75. The line is dashed, so the inequality is strict. "Left of the line" (for a line sloping up to the right) is the half-plane above the line, so

y > 2x + 0.75.

One example solution is (1, 3) because 3 > 2(1) + 0.75 = 2.75. (Also (0,1) works.)