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.
