The graph below shows the solution to a system of inequalitie

which of the following inequalities is modeled by the graph

Given the graph, we need to look for the equation of the line using the linear equation since the plot is obviously a line.

To do that, we need two points. The simplest points to locate are the two points that converges the x and y axes which are (3,0) and (4,0), respectively. Now we apply the linear equation formulation:

y = mx+b

First, we need to get the slope.

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

Since we know the slope, we need to look for the b which is also the y-intercept or the point at which x = 0.

So at x = 0, which point or value at y-axis hits with the line? It is the point (0,4).
Therefore, b = 4.

Completing the equation,

y = -(4/3)x + 4

or we can write it as

4x + 3y = 12.

Now to know which of the choices is correct, we simply assign values and see for ourselves which is true.

Let x = 2, so y = 2

4(2) + 3y = 12
8 < 12

If you assign more values, you will notice that 4x + 3y is always less than or equal to 12. Thus, the answer is letter a.

The answer is the third choice