Question

Express the statement as an equation. Use the given information to find the constant of proportionality.

y is directly proportional to x. If $\mathrm{x}=6$, then $\mathrm{y}=42$.

Short answer

Equation that represents the statement is $\mathrm{y}=\mathrm{kx}$.

Constant of proportionality is 7.

Step-by-step solution

Step 1. Understanding Direct variation.

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

For example:

$\mathrm{y}=\mathrm{kx}$

Here $\mathrm{k}\ne 0$, y is directly proportional to x and vice versa.

Step 2. Write the equation.

The relation between variables is proportional hence,

$\mathrm{y}=\mathrm{kx}$

Where k is constant of proportionality.

Step 3. Plug the values given in the equation to determine the value of the constant of proportionality.

Given values:

$\begin{array}{l}\mathrm{x}=6\\ \mathrm{y}=42\end{array}$

Putting values we get,

$\begin{array}{c}42=\mathrm{k}\left(6\right)\\ \mathrm{k}=\frac{42}{6}\\ \mathrm{k}=7\end{array}$