If the line goes through the origin and points (a, b) and (b, bc). What is the value of c?

c = b/a.

Step-by-step 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.