A tutor charges a total fee, C, in dollars, for a tutoring session of h hours according to… — SAT

A tutor charges a total fee, $C$ , in dollars, for a tutoring session of $h$ hours according to the equation $C = 25h + 40$ . What is the best interpretation of $40$ in this context?

A
The fee, in dollars, charged for each hour of tutoring
B
The total fee, in dollars, charged for a 1-hour tutoring session
The flat sign-up fee, in dollars, charged by the tutorCevap
D
The number of hours of tutoring for which the total fee is $0

Cevap

The flat sign-up fee, in dollars, charged by the tutor

The constant term in the linear equation represents the value of the dependent variable when the independent variable is zero. In this context, when the tutoring hours are zero, the total fee is 40 dollars, representing the flat sign-up fee.

Adım Adım Çözüm

Identify the structure of the linear equation

The equation

C = 25h + 40

matches the slope-intercept form

y = mx + b

The linear model consists of a variable term representing the hourly rate and a constant term representing the flat fee.

Determine the value of the constant term when the variable is zero

When

h = 0

, the equation simplifies to

C = 40

Setting the hours of tutoring to zero isolates the starting value of the function.

Interpret the starting value in the context of the problem

A session of

0

hours corresponds to the cost before any tutoring begins, which represents a flat initial sign-up fee of

40

Connecting the mathematical y-intercept to the real-world scenario identifies the interpretation of the constant.

Anahtar Kavram

Interpreting Linear Relationships in Context

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Cevap

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