Answer: c = b/a.
Explanation:
A line can be written as:
y = s*x + p
Knowing that this line goes through the origin (0, 0) we know that when x = 0 we must have y = 0.
then:
0 = s*0 + p
0 = p
Then our line is y = s*x.
Now, we know that this line goes trough:
(a, b) and (b, bc)
Now, whit this we can find the value of the slope:
S = (y2 - y1)/(x2 - x1)
using the pairs (0, 0) and (a, b) we also know that:
S = (b - 0)/(a - 0) = b/a
and knowing that goes trough the point (0, 0) and (b, bc)
the slope is:
S = (bc - 0)/(b - 0) = bc/b = c.
So we have that c = b/a.