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−9x12
Proportional
Constant of proportionality:
=k
Not proportional
(b)
=8x=y
Proportional
Constant of proportionality:
=k
Not proportional
Note: For equation (a), the actual equation was not provided. Therefore, the answer given for equation (a) is based on the assumption that the equation is of the form:
y = kx + b, where b is a constant and k is the constant of proportionality/variation.
(a) Assuming the equation is of the form y = kx + b:
Not proportional
(b) Proportional
Constant of proportionality: k = 8
To determine whether x and y are directly proportional, we need to check if the equation follows the form y = kx, where k is the constant of proportionality.
(a) The equation is y = -9x + 12, which does not follow the form y = kx. Therefore, for this equation, x and y are not directly proportional.
(b) The equation is 8x = y, which follows the form y = kx. Therefore, for this equation, x and y are directly proportional. And the constant of proportionality, k, is equal to 8.