For each equation, determine whether

x
and
y
are directly proportional (that is, if the equation shows direct variation).
If so, then find the constant of proportionality (the constant of variation).
(a)
=y−x

Proportional
Constant of proportionality:
=k



Not proportional
(b)
=y75x

Proportional
Constant of proportionality:
=k



Not proportional

1 answer

Note: An equation shows direct variation if it can be written in the form y = kx, where k is a constant of proportionality.

(a) y = k(x-1) - This equation is not in the form y = kx, so it does not show direct variation.

(b) y = (75)x - This equation can be written in the form y = kx by setting k = 75. Therefore, x and y are directly proportional with a constant of proportionality k = 75.