Evaluating Formulas by Substitution

As we mentioned, a formula has a dependent variable on one side and an expression involving the independent variable(s) on the other side. To evaluate a formula, we evaluate the expression containing the independent variable(s). The result is the value of the dependent variable. Ready, Miss Independent? Let's make you Miss Dependent.

Sample Problem

Consider the formula C = 5xy. Find C if x = 2 and y = 3.

Since C is the dependent variable, that'll be our result. Now, how do we find its value? We evaluate the expression on the other side of the equal sign, 5xy, for x = 2 and y = 3.

C = 5(2)(3) = 30

We now know C's value is 30. However, we don't know if that's in dollars or pesos—no getting excited just yet.

We can use formulas to answer all sorts of questions. Like, "Why is the sky blue?" or "What makes birds sing?" or "What happened to Julia Stiles' career?" More practically, they can help us solve something like the problem below.

Sample Problem

Find the area of a square with sides that are 4 cm long.

The area of a square is given by the formula A = s2, where A is the area of the square and s is the length of a side. In this case, the length of a side is 4, and we substitute 4 for s and evaluate the area formula:

A = (4)2 = 16 cm2

We will now let r represent rock star, which is what we are for finding the area of this square.