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On a graph the cost of renting a car is based on the distance traveled

Distance in miles is x value and y is the rental cost in dollars
On graph (0,20) and (20,25)
f(x)=

3 answers

To determine the function \( f(x) \) that represents the rental cost based on the distance traveled, we can observe the two points given: \( (0, 20) \) and \( (20, 25) \). Here's how we can find the linear function:

  1. Identify the points:

    • Point 1: \( (0, 20) \) means that when no distance is traveled (0 miles), the cost is $20.
    • Point 2: \( (20, 25) \) means that when 20 miles are traveled, the cost is $25.

  2. Calculate the slope (m) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (0, 20) \) and \( (x_2, y_2) = (20, 25) \): \[ m = \frac{25 - 20}{20 - 0} = \frac{5}{20} = \frac{1}{4} \]

  3. Use the point-slope form of the line: The point-slope form of a line is given by \[ y - y_1 = m(x - x_1) \] Plugging in \( m = \frac{1}{4} \) and using the point \( (0, 20) \): \[ y - 20 = \frac{1}{4}(x - 0) \] Simplifying this gives: \[ y - 20 = \frac{1}{4}x \] \[ y = \frac{1}{4}x + 20 \]

  4. Final function: Thus the function \( f(x) \) that relates the distance traveled \( x \) to the rental cost \( f(x) \) is: \[ f(x) = \frac{1}{4}x + 20 \]

This function indicates that the initial cost of renting the car is $20, and there is an additional charge of $0.25 for each mile traveled.

1/4x is not right

I apologize for any confusion. Let's revisit the calculation for the linear function that represents the cost of renting a car based on the distance traveled.

Given the points:

  • Point A: \( (0, 20) \)
  • Point B: \( (20, 25) \)

  1. Calculate the slope (m): Using the formula for slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the coordinates: \[ m = \frac{25 - 20}{20 - 0} = \frac{5}{20} = \frac{1}{4} \]

  2. Finding the equation of the line: We know the slope \( m = \frac{1}{4} \) and we can take the first point \( (0, 20) \) to find the equation using the point-slope formula: \[ y - y_1 = m(x - x_1) \] Substituting the slope and point values: \[ y - 20 = \frac{1}{4}(x - 0) \] Simplifying this gives: \[ y - 20 = \frac{1}{4}x \] \[ y = \frac{1}{4}x + 20 \]

  3. Final function: Thus, the function \( f(x) \), which gives the rental cost based on the distance \( x \), is indeed: \[ f(x) = \frac{1}{4}x + 20 \]

If this interpretation does not match your expectations or if there’s a specific licensing agreement or aspect you want me to consider differently, please let me know, and I’ll adjust the function accordingly!