incorrect answers for (b) & (c)

(b)
from the diagram,
point B is left side of origin, so should be ...
coordinates of B = (-5,0)

note : coordinates of C = (2,0)

(c)
when a straight line slants from top left to bottom right, gradient must be negative.
when a straight line slants from bottom left to top right, gradient must be positive.

gradient AB = (10-0)/(0-(-5)) = 2 [ positive ! ]
sub (2,0) into equation
(0) = (2)(2) + c
c = -4
equation of line passing through C is y = 2x-4