Answer:
The answer is D. [tex]y = \frac{x-4}{x+2} \\y = x-4[/tex]
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 [tex]y1 = \frac{x+4}{x+2}[/tex] and [tex]y=2\frac{x-4}{x+2}[/tex], if we test x=-1.
[tex]y1=\frac{-1+4}{-1+2}=\frac{3}{1}=3[/tex] 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:
[tex]y1=\frac{-1-4}{-1+2}=\frac{-5}{1}=-3[/tex] 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) = [tex]\frac{8}{6}[/tex] and y2 (x=4) = 0
