Dotted line joining negative 1, negative 2 and 3,0 and the region below the line is shaded. which of the following inequalities is best represented by this graph?

a) x − 2y > 3
b) x − 2y < 3
c) 2x − y > 3
d) 2x − y < 3

The two points are (-1,-2) and (3,0). Let's find the slope of the line through these points

m = (y2 - y1)/(x2 - x1)
m = (0 - (-2))/(3 - (-1))
m = (0 + 2)/(3 + 1)
m = 2/4
m = 1/2

Plug this m value and one of the points into the equation y = mx+b. Solve for b. I'll use (x,y) = (-1,-2) as the point of choice

y = mx+b
-2 = (1/2)*(-1)+b
-2 = -1/2+b
-2+1/2 = b
b = -4/2+1/2
b = -3/2

So the boundary line equation is y = (1/2)x-3/2
The shading is below the boundary line equation. The boundary is dashed. So we have this inequality y < (1/2)x - 3/2
Now we must get the inequality either in the form Ax+By < C or Ax+By > C

Let's do that to get...
y < (1/2)x - 3/2
2y < x - 3
-x+2y < -3
-1*(-x+2y) > -1*(-3)
x-2y > 3

Therefore, the final answer is choice A) x-2y > 3

See attached for a graph

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