To determine the meaning of the initial amount in the equation describing the technician's charges, we need to interpret what the initial amount represents. In equations of the form \( y = mx + b \) (where \( b \) is the fixed amount and \( m \) is the charge per hour), the initial amount \( b \) usually refers to the fixed charge that is incurred regardless of the number of hours worked on the repair.
Given the options provided, the answer that aligns with this interpretation would be:
B. It means the technician charges a fixed amount of $45 for the repair.
However, since the options seem to suggest values (45, 75), if the context indicates that the fixed amount mentioned in the question aligns with either of these amounts, one would have to confirm from the setup of the equation in the question. Assuming you are referring to the technician's fixed charge as $45, then option B is the accurate choice. If it were $75, the option would need to be adjusted accordingly.
Without the specific equation to reference, it's critical to confirm what the initial (fixed) amount is within that context.