Answer:
2x − 3y < 7
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.