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

2x − 3y < 7

Step-by-step explanation:

You can write the inequality equation for the graph using the form y - y1 = m(x + x1). The inequality line has a point at (5,1). It also has a slope of 2/3 since the line moves up 2 and over 3 to the next point on the line.

This means the lines equation is y - 1 = 2/3(x - 5). You can convert it into standard form by simplifying.

y - 1 = 2/3(x - 5)

y - 1 = 2/3x - 10/3

y = 2/3x - 7/3                       To clear the fraction multiply by 3.

3y = 2x - 7

-2x + 3y = -7                        Change the negative on the x by multiplying by -1

2x - 3y = 7

But since this is an inequality, you must use an inequality sign. Since the line is dashed it is not equal to. Your options are < and >.  Use the point (0,0) to test which sign is appropriate.

2x - 3y > 7                     2x - 3y < 7

2(0) - 3(0) > 7                 2(0) - 3(0) < 7

0 > 7                               0 < 7

Since (0,0) is a solution, the answer is 2x - 3y < 7.

step-by-step explanation: