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.
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
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