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Zorluk: OrtaInterpreting Linear Relationships in Context

A software developer uses the equation P=1500+45nP = 1500 + 45n to calculate the total price PP, in dollars, charged to a client for a project, where nn represents the number of hours spent debugging the software. Which of the following is the best interpretation of the number 4545 in this context?

  1. The increase in the total price, in dollars, for each additional hour spent debugging the softwareCevap
  2. B
    The initial price, in dollars, charged for the project before any hours are spent debugging
  3. C
    The number of additional hours spent debugging for each 1-dollar increase in the total price
  4. D
    The total price, in dollars, charged for a project that requires exactly 1 hour of debugging

Cevap

The increase in the total price, in dollars, for each additional hour spent debugging the software
The coefficient of nn in the equation P=1500+45nP = 1500 + 45n is 4545, which represents the slope of the line. The slope measures the rate of change of the dependent variable, PP (total price in dollars), per unit change in the independent variable, nn (hours spent debugging). Thus, 4545 represents an increase of 45 dollars in the total price for each additional hour spent debugging.

Adım Adım Çözüm

1
Identify the structure of the linear equation.
The equation P=1500+45nP = 1500 + 45n is in the slope-intercept form y=mx+by = mx + b, where PP is the dependent variable (equivalent to yy), nn is the independent variable (equivalent to xx), the coefficient 4545 is the slope mm, and the constant 15001500 is the y-intercept bb.
Understanding the components of a linear equation helps map them to their real-world meanings.
2
Interpret the meaning of the slope in context.
The slope m=45m = 45 represents the rate of change of the dependent variable PP (total price in dollars) with respect to the independent variable nn (hours spent debugging). This means that for each unit increase in nn (1 additional hour of debugging), PP increases by 4545 units (45 dollars).
The coefficient of the independent variable in a linear model represents the unit rate of change.

Anahtar Kavram

Interpreting the slope of a linear model in context
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Konular

Interpreting Linear Relationships in Context

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