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Difficulty: EasyInterpreting Linear Relationships in Context

To rent an electric scooter, a rider pays a flat unlocking fee plus a fee for each minute of the ride. The total cost CC, in dollars, for a ride of mm minutes is given by the equation C=0.15m+1.20C = 0.15m + 1.20. Which of the following is the best interpretation of the number 1.201.20 in this context?

  1. A
    The cost, in dollars, for each minute of the scooter ride
  2. The flat unlocking fee, in dollars, to rent the scooterAnswer
  3. C
    The total cost, in dollars, of a scooter ride that lasts 1 minute
  4. D
    The cost, in dollars, for a ride that lasts 15 minutes

Answer

The flat unlocking fee, in dollars, to rent the scooter
In the linear model C=0.15m+1.20C = 0.15m + 1.20, the constant term 1.201.20 represents the value of CC when m=0m = 0. Since mm represents the number of minutes, m=0m = 0 corresponds to the beginning of the rental. Therefore, 1.201.20 represents the initial flat unlocking fee, in dollars, to rent the scooter.

Step-by-Step Solution

1
Identify the component of the linear equation C=0.15m+1.20C = 0.15m + 1.20 that corresponds to the number 1.201.20.
The number 1.201.20 is the constant term (y-intercept) of the equation.
A linear equation in slope-intercept form is y=mx+by = mx + b, where bb is the y-intercept (the value of yy when x=0x = 0).
2
Determine the physical meaning of m=0m = 0 in the given context.
m=0m = 0 represents a ride that lasts 00 minutes, meaning no time has elapsed yet.
Evaluating the relationship at the initial state helps identify the physical meaning of the y-intercept.
3
Substitute m=0m = 0 into the equation to find the corresponding cost.
C=0.15(0)+1.20=1.20C = 0.15(0) + 1.20 = 1.20 dollars.
This shows that the initial cost, or flat unlocking fee before starting the ride, is 1.201.20 dollars.

Key Concept

Interpreting the y-intercept of a linear relationship in context
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Topics

Interpreting Linear Relationships in Context

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