Question

Which is the graph of the solution set of −2x + 5y > 15?

On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 3) and (10, 7). Everything above and to the left of the line is shaded.

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (5, 1). Everything below and to the left of the line is shaded.

On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 5) and (10, 9). Everything above and to the left of the line is shaded.

Answer 1

Rewrite: 5y > 2x + 15 ⇒ y > (2/5)x + 3.

Boundary is the dashed line y = (2/5)x + 3 (slope 2/5, y-intercept 3), which passes through (0,3) and (10,7). Because the inequality is >, shade the half-plane above the line.

So the first graph is correct.