Chapter 7, Problem 1TE

If y is proportional to x, and y = 12x, what is the constant of proportionality?

To determine

The constant of proportionality if $y$ is proportional to $x$ and $y=12x$.

Answer to Problem 1TE

The constant of proportionality is $k=12$.

Explanation of Solution

Definition used:

Two variables $x$ and $y$ are proportional to each other (or directly) if their quotient is constant. That is, $y$ is directly proportional (or simply proportional) to $x$ if $y$ and $x$ are related by the equation $\frac{y}{x}=k$ or, equivalently, $y=kx$ where $k\ne 0$ s called the constant of proportionality.

Calculation:

Given that $y$ is proportional to $x$ and $y=12x$.

The equation $y=12x$ can be rewrite as $\frac{y}{x}=12$.

Compare this equation with $\frac{y}{x}=k$.

Therefore it is obtained that $k=12$.

By the definition stated above, $k=12$ is the constant of proportionality.

Therefore, the constant of proportionality is $k=12$.