To determine the correct options regarding the linear function \( f(d) \) modeling the taxi ride cost based on the given data, we can start by finding the slope and y-intercept of the linear equation in slope-intercept form, \( f(d) = md + b \), where \( m \) is the slope and \( b \) is the y-intercept.
We know that:
- For \( d = 2 \), \( f(2) = 6 \)
- For \( d = 4 \), \( f(4) = 10 \)
Step 1: Calculate the slope (m)
The slope \( m \) is calculated as:
\[ m = \frac{f(4) - f(2)}{4 - 2} = \frac{10 - 6}{2} = \frac{4}{2} = 2 \]
Step 2: Determine the y-intercept (b)
We can use one of the points to find \( b \). Let's use the point \( (2, 6) \):
\[ f(2) = m \cdot 2 + b \ 6 = 2 \cdot 2 + b \ 6 = 4 + b \ b = 6 - 4 = 2 \]
So, the cost function is:
\[ f(d) = 2d + 2 \]
Step 3: Validate the function with both points
Now, we'll check if our function gives the correct outputs for both distances.
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For \( d = 2 \): \[ f(2) = 2(2) + 2 = 4 + 2 = 6 \]
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For \( d = 4 \): \[ f(4) = 2(4) + 2 = 8 + 2 = 10 \]
Both values match correctly with the given data.
Conclusion:
Using this function, we can derive information to answer what might be true of the taxi rides.
Since the function is linear, properties we can derive include:
- The cost increases by a fixed amount for each additional mile (the slope);
- There exists a cost (2 dollars) when no miles are traveled (the vertical intercept).
With this analysis, you need to check the provided options (A, B, C, D, E, F) and identify which align with the established function \( f(d) = 2d + 2 \). However, since the options themselves were not included, I can't directly state which ones are correct without that information.
If you provide the options, I can help further determine which ones are true!
2 answers