Question

Which inequality matches the graph?
Choices:
-2x + 3y > 7
2x - 3y < 7
-3x + 2y ≥ 7
3x - 2y ≤ 7

Answer 1

Graph

Answer 2

Without solving, simply inspect each inequality using the standard form:
y=mx+b (m - slope, b - where the line intersects y)
Convert all 4 to a semi-standard form:

A) 3y > 2x+7
B) 3y < 2x-7
C) 2y ≥ 3x+7
D) 2y ≤ 3x-7

According to the graph, the inequality intersects y below the x axis, so we know for sure it's not A or C.
Convert the remaining 2 to an actual standard form:

B) y < 2/3x-7/3
D) y ≤ 1.5x-3.5

According to the graph again, the intersection with y happens at -2.something, so we can tell for sure it's not D.

B) 3y < 2x-7