The problem does not specify whether it is a proportional variation or an inversely proportional variation, so both cases will be solved.
case a) proportional variation
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
\(\frac{y}{x} =k\)
Find the value of k
\(y=6\\ x=30\\ k=\frac{6}{30} =\frac{1}{5}\)
Find the value of y for x=\(15\)
\(y=kx\\ y=\frac{1}{5} *15\\ y=3\)
the answer case a) is
\(y=3\)
case b) inverse variation
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
\(yx =k\)
Find the value of k
\(y=6\\ x=30\\ k=30*6=180\)
Find the value of y for x=\(15\)
\(yx=k\\ y=\frac{180}{15}\\ y=12\)
the answer case b) is
\(y=12\)
