Skill: Identify the initial value of a linear relationship

The initial value is the value of the dependent variable, $y$, when the independent variable, $x$, is $0$. In an equation of the form

$$y=mx+b,$$

the initial value is $b$, the constant term. It is also the $y$-intercept.

Example: A taxi fare is modeled by

$$C=2.50m+4,$$

where $m$ is the number of miles traveled and $C$ is the cost in dollars.

1. Identify the independent variable: $m$, the miles traveled.
2. Identify the dependent variable: $C$, the cost.
3. Look for the value of $C$ when $m=0$:

$$C=2.50(0)+4$$ $$C=4$$

4. Therefore, the initial value is $\boxed{4}$ dollars.

This means the taxi costs 4$before any miles are traveled. The number$2.50$ is the rate of change, or the cost per mile, not the initial value.