Question

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

S is proportional to the product of p and q. If$p=4$and $q=5$, then $S=180$.

Short answer

Equation that represents the statement is $S=k\left(pq\right)$.

.Constant of proportionality is 9.

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:

$y=kx$

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

Step 2. Write the equation.

The relation between variables is proportional hence,

$S=k\left(pq\right)$

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:

$\begin{array}{l}S=180\\ p=4\\ q=5\end{array}$

Putting values we get,

$\begin{array}{l}180=k\left(4\times 5\right)\\ 180=k\left(20\right)\\ k=\frac{180}{20}\\ k=9\end{array}$