In this context, the equation given is $y = mx + b$, where $y$ represents the total cost for $x$ miles, $m$ is the rate per mile, and $b$ is the base or starting cost.

Here:

• The shuttle service charges a base fee of $15, which represents $b$.
• The cost per mile is $1.15, which represents $m$.

Thus, the value of $m$ is 1.15 in this context, as it is the rate charged per mile traveled.

Would you like more details or have any further questions?

Here are related questions to consider:

1. How would you interpret the value of $b$ in this equation?
2. How would the equation change if the base fee were $20 instead?
3. What would the cost be for a 10-mile trip using this equation?
4. How would the cost structure change if the per-mile charge doubled?
5. Can you graph the relationship between miles and cost with this equation?

Tip: In linear equations, $m$ often represents a rate of change or slope, indicating how much $y$ changes per unit increase in $x$.