What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Blue Cab?

To determine the equation in **slope-intercept form** that relates the cost ($C$) to the miles traveled ($m$) for a Blue Cab, we follow the general formula for a linear relationship:

\[
C = mx + b
\]

Where:
- $C$ is the **cost**,
- $m$ is the **slope** (which represents the cost per mile),
- $x$ is the **miles traveled**, and
- $b$ is the **y-intercept** (the initial cost or base fee, often called a flat fare).

### Steps to find the equation:
1. **Determine the base cost (if applicable):** This is the value of $b$, the fixed cost when no miles have been traveled.
2. **Find the cost per mile:** This is the value of $m$, which tells us how much the fare increases for each mile driven.

If we have the values for the base cost and cost per mile, we can substitute them into the equation.

For example, if:
- the base cost $b$ is $3 (initial charge), and
- the cost per mile $m$ is $2 per mile,

Then the equation would be:

\[
C = 2x + 3
\]

Where $C$ is the total cost, and $x$ represents the number of miles traveled.

### Do you have specific values for the base fare and cost per mile?

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Would you like to explore further details or adjustments?  
Here are five related questions you might be interested in:

1. How do you find the slope when you know two cost points?
2. What if the base fare is $0—how would the equation change?
3. How can we use this equation to predict the cost for 15 miles?
4. How do changes in base fare affect the overall cost formula?
5. How can we graph the cost function for visualization?

**Tip:** Always double-check the base fare and cost per mile to ensure the correct equation is derived!

What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Blue Cab?

Discover how to find the slope-intercept equation that relates cost to miles traveled for a Blue Cab. This guide explains key concepts like base fare, cost per mile, and linear equations in algebra. Ideal for students in Grades 6-9.

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