Question

Jada and Lin are comparing inches and feet. Jada says that the constant of proportionality is 12. Lin says it is 1/12. Do you agree with either of them? 12 Explain your reasoning.

Answer 1

When two variables have a proportional relationship, this means one is equal to the other times a constant of proportionality. If we have a variable y proportional to x, then

$y=kx$

Where k is a constant of proportionality.

In our problem, we are comparing inches and feet. We know that

$ft=12in$

In this case, we have a proportional relationship, with 12 as the constant of proportionality, however, we can write this equality also as

$in=\frac{1}{12}ft$

Which is also a proportional relationship, with 1/12 as the constant of proportionality.

This means both Jada and Lin are correct, the constant of proportionality depends if you're writing feet as a function of inches, or inches as a function of feet.