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Zorluk: OrtaInterpreting Linear Relationships in Context

A ride-share driver uses a mobile application to track their daily net earnings. The driver's net earnings, EE, in dollars, after completing nn rides in a day can be modeled by the equation E=18n−25E = 18n - 25. Which of the following is the best interpretation of the number 2525 in this context?

  1. A
    The driver's net earnings, in dollars, for each completed ride.
  2. The driver's daily starting cost, in dollars, before any rides are completed.Cevap
  3. C
    The driver's net earnings, in dollars, after completing exactly one ride.
  4. D
    The number of completed rides for which the driver's net earnings are equal to 0 dollars.

Cevap

The driver's daily starting cost, in dollars, before any rides are completed.
In the linear equation E=18n−25E = 18n - 25, the variable EE represents net earnings and nn represents the number of rides. The constant term −25-25 represents the value of EE when n=0n = 0. In this context, starting with −25-25 dollars in net earnings means the driver has a daily starting cost or fee of 2525 dollars before completing any rides.

Adım Adım Çözüm

1
Identify the component of the linear equation E=18n−25E = 18n - 25 associated with the number 2525.
The number 2525 is part of the constant term −25-25 in the equation.
Linear equations in context are typically written in the form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
2
Determine the contextual meaning of the constant term (y-intercept) in this model.
The constant term −25-25 represents the value of EE when n=0n = 0.
Setting the independent variable nn (number of rides) to 00 gives the starting value of the dependent variable EE (net earnings).
3
Interpret the negative value in terms of daily operations.
An initial net earning of −25-25 dollars means the driver starts with a cost or loss of 2525 dollars.
A negative starting value indicates a cost or fee that must be paid before any revenue is generated.

Anahtar Kavram

Interpreting the y-intercept of a linear model in context.
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Konular

Interpreting Linear Relationships in Context

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