Skill: Represent relationships using equations

An equation shows how one quantity depends on another.

1. Choose variables.
   Let $x$ be the number of hours a bike is rented.
   Let $y$ be the total cost in dollars.

2. Find the rate of change.
   The bike costs 3$for each hour, so the cost increases by$3$when$x$increases by$1$. This gives the term$(3x)$.

3. Find the starting amount.
   There is a 5$starting fee, even when the bike is rented for$0$hours. This is the constant$5$.

4. Write the equation.

$$y=3x+5$$

This equation means: multiply the number of hours by $3$, then add the starting fee of $5$.

Check the equation: If the bike is rented for $4$ hours, substitute $(x=4)$:

$$y=3(4)+5=12+5=17$$

The total cost is 17$, which agrees with the description. Here,$3$is the rate of change, and$5$ is the initial value.