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.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

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step-by-step explanation: