Question

The graph below shows the solution to a system of inequalitie

Answer 1

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.