The cost of a taxi journey per mile can be modelled using the straight line y = 1.5x + 4. An 8 mile journey costs £16 find the minimum taxi fare

The cost of a taxi journey is modeled by the linear equation:

\[
y = 1.5x + 4
\]

where:
- \( y \) is the total cost of the journey in pounds,
- \( x \) is the number of miles traveled.

### Step 1: Calculate the cost for an 8-mile journey

We are told that an 8-mile journey costs £16. Substituting \( x = 8 \) into the equation:

\[
y = 1.5(8) + 4
\]
\[
y = 12 + 4 = 16
\]

So, the equation holds true for an 8-mile journey costing £16.

### Step 2: Find the minimum taxi fare

The minimum taxi fare occurs when the distance \( x \) is zero (no miles traveled). Substituting \( x = 0 \) into the equation:

\[
y = 1.5(0) + 4 = 4
\]

Thus, the minimum taxi fare is **£4**, which is the base fare before any miles are traveled.

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Would you like further details or have any questions?

Here are 5 related questions:
1. What is the cost of a 5-mile taxi journey using the same model?
2. How would the model change if the base fare increased to £5?
3. How can you determine the number of miles for a journey costing £20?
4. How does the slope of the line affect the rate per mile?
5. Can you use the equation to model different types of vehicle fares?

**Tip:** The slope of a line in linear equations represents the rate of change, which in this case is the cost per mile.

The cost of a taxi journey per mile can be modelled using the straight line y = 1.5x + 4. An 8 mile journey costs £16. Find the minimum taxi fare.

Explore how to determine the minimum taxi fare using the linear equation y = 1.5x + 4. This problem demonstrates the use of slope-intercept form, calculating costs for a journey, and understanding base fare. Suitable for students in Grades 6-8.

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