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, for a repair that takes x hours.

Question

y=45x+75
What is the meaning of the y-intercept of the equation?
A.It means the technician charges a fixed amount of $45 for the repair
B.It means the technician charges a fixed amount of $75 for the repair.
C. It means the technician charges $45 per hour for the repair.
D. It means the technician charges $75 per hour for the repair.

Answer 1

To understand the meaning of the y-intercept in the equation \( y = 45x + 75 \), we look at the value of \( y \) when \( x = 0 \). The y-intercept occurs where the line crosses the y-axis, which is when the number of hours worked is zero.

Substituting \( x = 0 \) into the equation:

\[ y = 45(0) + 75 = 0 + 75 = 75 \]

This means that when no hours are worked (i.e., \( x = 0 \)), the total charge \( y \) is $75. This $75 represents the fixed cost charged by the technician for the repair, regardless of the time spent on it.

So, the correct interpretation of the y-intercept is:

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