Question

A computer technician charges a fixed amount for a repair, plus an additional amount per hour. The equation below describes y, the total amount the technician charges, in dollars, based on x hours for the repair.


What is the meaning of the initial amount for the equation?

A.

It means the technician charges $45 per hour for the repair.

B.

It means the technician charges a fixed amount of $45 for the repair.

C.

It means the technician charges a fixed amount of $75 for the repair.

D.

It means the technician charges $75 per hour for the repair.

Answer 1

y=45x+75

Answer 2

To determine the meaning of the initial amount in the equation that describes the total amount charged by the technician, we need to understand that the initial amount represents a fixed charge, independent of the number of hours worked.

Thus, if we assume the equation is in the format:

\[ y = mx + b \]

where:
- \( y \) is the total amount charged,
- \( m \) is the additional amount charged per hour,
- \( x \) is the number of hours,
- \( b \) is the initial fixed charge.

If $45 is the initial amount or fixed charge, that would be represented by \( b \), meaning the technician charges a fixed amount of $45 for the repair. If $75 is the initial amount, it would imply that the fixed charge is $75.

Since the options provided suggest that the initial amount being referred to is $45 and $75, we look for the correct interpretation based on typical representations.

Hence:

- If \( b = 45 \), the answer would be **B**: It means the technician charges a fixed amount of $45 for the repair.
- If \( b = 75 \), the answer would be **C**: It means the technician charges a fixed amount of $75 for the repair.

In the absence of knowledge regarding the exact initial amount, we can choose these accordingly. Therefore, without additional context from the equation:

If the fixed amount is indeed $45, **B** is correct.

If the fixed amount is $75, **C** is the correct.

Since we don't have the actual equation, we can't pinpoint whether **B** or **C** is definitively right without further information.

Answer 3

Thank you for providing the equation \( y = 45x + 75 \).

In this equation:
- \( y \) represents the total amount charged.
- \( x \) represents the number of hours for the repair.
- \( 45 \) is the coefficient of \( x \), which indicates the additional charge per hour.
- \( 75 \) is the constant term, which represents the fixed charge or initial amount for the repair.

Given this, the initial amount (the constant term, 75) indicates that the technician charges a fixed amount of $75 for the repair.

So the correct interpretation is:

**C. It means the technician charges a fixed amount of $75 for the repair.**