Question

Which system of equations is represented by the graph?

Answer 1

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The system of equations is represented by the graph is B. y = x plus 4, over x plus 2
y = x − 4

Answer 2

Answer:

The answer is D. $y = \frac{x-4}{x+2} \\y = x-4$

Step-by-step explanation:

Let's start by eliminating some wrong answers testing the values you are given in the red slope: (4, 0) and (-1, -5), taking into account that the coordinates are presented in the (x, y) format.

The options are y1=x+4 and y2=x-4

For (4, 0), x=4 so making the substitution x=4 in y1, we have y1= 4+4 = 8 or (4, 8), and (4, 0) ≠ (4, 8) thus all options showing y = x+4 can be discarded, leaving only B. and D.

Now let's test (-1, -5), with x=-1.

The options are $y1 = \frac{x+4}{x+2}$ and $y=2\frac{x-4}{x+2}$, if we test x=-1.

$y1=\frac{-1+4}{-1+2}=\frac{3}{1}=3$ So for y1 (x=-1) = 3, thus (-1, 3). this discards option B, leaving option D. the only possible answer.

But still, running a test to see if D fits:

$y1=\frac{-1-4}{-1+2}=\frac{-5}{1}=-3$ So y2 (x=-1) = -5, thus (-1, -5) just like we see in the image. This also fits with the other coordinate (4, 0), since y1 (x=4) = $\frac{8}{6}$ and y2 (x=4) = 0