Answer:
C. y= -4/5x-2.
Explanation:
The points are(-5, 2) and (5, -6). We will put this in place of the variables x and y. -5 and 5 are x and 2 and -6 are y the equations are y= -5/4x-2, y=4/5x+2, y= -4/5x-2, and y=5/4x+2. We will do the equations one by one till we get to the right one. Let start with y= -5/4x-2 first. We put -5 and 2 in for the variables like this: 2= -5/4(-5)-2, and now we calculate it to see if it will be equal on both sides, 2=25/4 -2, 25/4 is the same as 6.25, 2=6.25-2 and that came out to be 2=4.25 which didn't equal each other as you see, since (-5, 2) don't work, there is no reason to try the other pair of numbers (5, -6). We will just go to the next equation y=4/5x+2. We put -5 and 2 in for the variables like we did before and see if it will be equal on both sides, 2=4/5(-5)+2, 2= -4+2, 2= -2. The equation is not equal as you see on this one, so there is no reason to try the other pair of numbers (5, -6) on this equation either. The next equation is y= -4/5x-2. We put -5 and 2 in for the variables once more, so now it looks like this: 2= -4/5(-5) -2 and calculate it of course, 2=4-2, 2=2, (-5, 2) works. We want to make sure that both pair of numbers work, so we will do (5, -6) also, we put 5 and -6 in for the variables like what we did with the other pair. The equation will looks like this now: -6= -4/5(5) -2. Now we calculate it -6= -4-2, -6= -6, the equation is equal, (5, -6) works also. So the answer to this question is C. y= -4/5x-2.