Vladimir says that the equation of the line that passes through points (-5,-3) and (10,9) is y=4/5x+1. robyn says that the line passes through the points (-10,-7) and (-15,-11). who is correct? a)only vladimir b)only robyn c)both vladimir and robyn d)neither vladimir nor robyn

The slope given by Vladmir's points =  (9--3)/10--5) = 12/15 = 4/5
so its equation is 
y - y1 = (4/5)(x - x1)   where (x1,y1) = (10,9) giving:-
y - 9 = (4/5)(x - 10)
y = 4/5 x =1    which is the required equation 

So Vladimir is right.

Testing if  Robyn is right:-
Plug in his values:-
-7 = 4/5*-10  + 1
-7 = -7   so that point is on the line

-11 = (4/5) * -15 + 1
-11 = -11 so this point is also on the line

-  c) Both are right