Analyzing One-Variable Relationships in Context

First, it can be helpful to highlight the information given about the situation.

• The total cost for the taxi ride is $$46.37.$
• The cost per mile traveled is $$1.73.$
• There is a starting fee of $$4.85.$

A variable can be used to represent the unknown quantity in the situation.
Here, the unknown quantity is the length of the ride. Thus, the variable $m$ will be used to represent the number of miles traveled.

Next, it is necessary to understand how the different quantities in the problem relate.
The ${\color{#0000FF}{\text{total cost}}}$ includes the ${\color{#009600}{\text{starting fee}}}$ and the cost of the miles traveled. Additionally, the cost of the miles traveled can be found by multiplying the ${\color{#FF0000}{\text{cost per mile}}}$ by the ${\textcolor{purple}{\text{distance traveled}}}.$ As a verbal equation, this relationship can be expressed as follows. ${\color{#0000FF}{\text{total cost}}} = \text{{\color{#009600}{starting fee}}} + {\color{#FF0000}{\text{cost per mile}}} \cdot \textcolor{purple}{\text{distance}}$

Creating the equation involves translating the relationship from Step 3 into symbols. To do this, replace each quantity with the corresponding value.
For this situation, the following equation can be written. $\begin{aligned} {\color{#0000FF}{\text{total cost}}}\ =& \ \ \text{{\color{#009600}{starting fee}}} + {\color{#FF0000}{\text{cost per mile}}} \cdot \textcolor{purple}{\text{distance}}\\ &{\color{#0000FF}{46.37}}={\color{#009600}{4.85}}+{\color{#FF0000}{1.73}}\cdot \textcolor{purple}{m} \end{aligned}$