Question

Find y when x=15 if y=6 when x=30

Answer 1

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

$y=12$

Answer 2

The answer is y = 12 when x = 30. You can prove this through some properties of mathematics. Multiply 6 by 2 if x = 30. 30 is two times 15, so it makes sense.
Hope that answered your question.