Chapter 1.11, Problem 1E

If the quantities x and y are related by the equation y = 3x, then we say that y is _______________ _______________ to x and the constant of _______________ is 3.

To determine

To fill: The relation of the quantity $y$ to the quantity $x$ and the term used for constant 3 if the quantities x and y are related by $y=3x$.

Answer to Problem 1E

The quantity $y$ is directly proportional to the quantity $x$ and constant of proportionality is 3.

Explanation of Solution

If the quantities $x$ and $y$ are related by an equation,

$y=kx$ (1)

For some constant $k\ne 0$, we say that $y$ varies directly as $x$, or $y$ is directly proportional to $x$. The constant $k$ is called the constant of proportionality.

The given equation is,

$y=3x$ (2)

Compare the equation (2) with equation (1) to infer that y is directly proportional to x and 3 is called the constant of proportionality.

Therefore, the quantity $y$ is directly proportional to the quantity $x$ and constant of proportionality is 3.