https://file.aiquickdraw.com/mathbot/file/1730040789431unz5ml93.jpg

To find the formula for \( C \) in terms of \( n \) from the graph:

1. **Identify the starting cost (y-intercept):** From the graph, the cost when \( n = 0 \) miles is £2. This represents a fixed starting cost.

2. **Calculate the rate of increase (slope):** We need to determine how much the cost \( C \) increases for each additional mile \( n \). From the graph:
   - At \( n = 0 \), \( C = 2 \)
   - At \( n = 1 \), \( C = 3.6 \)
   
   The increase in cost per mile is:
   \[
   \text{slope} = \frac{3.6 - 2}{1 - 0} = 1.6
   \]
   
   Thus, for every mile, the cost increases by £1.6.

3. **Form the equation:** Using the slope-intercept form \( C = mn + b \), where \( m \) is the slope and \( b \) is the y-intercept:
   \[
   C = 1.6n + 2
   \]

So, the formula for \( C \) in terms of \( n \) is:
\[
C = 2 + 1.6n
\]

This matches the formula given in the answer box on the image.

Would you like further details on the slope calculation or other concepts?

Here are some related questions:
1. What is the meaning of the slope in this context?
2. How would the formula change if the initial fee were higher or lower?
3. Can you calculate the cost for a 10-mile journey using this formula?
4. How would you describe the relationship between \( C \) and \( n \) in mathematical terms?
5. What happens to the cost if the rate per mile increases?

**Tip:** When determining a formula from a graph, always identify the y-intercept and the slope (rate of change) first.

The graph shows the cost of some taxi journeys. Work out a formula for C in terms of n.

Learn how to determine the formula for the cost of a taxi journey based on distance. This problem covers key algebraic concepts, including the slope-intercept form and cost per mile calculations. Suitable for students in Grades 6-8.

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