Question

A computer technician charges a fee of $50 to diagnose a problem and $70 per hour to fix it. Write an equation in slope-intercept form to represent this situation. Identify the initial value and the rate of change.

Show your work.

(1 pt)
Responses

The initial value if $70 and the rate of change is $50.
The initial value if $70 and the rate of change is $50.

The rate of change is $120.
The rate of change is $120.

The initial value is $50 and the rate of change is $70.
The initial value is $50 and the rate of change is $70.

The initial value is $120.

Answer 1

To write an equation in slope-intercept form (y = mx + b) that represents the charges of the computer technician, we first need to understand the components of the charges:

1. **Initial fee (b)**: This is the fixed fee that the technician charges for diagnosing the problem, which is $50.
2. **Rate of change (m)**: This is the hourly rate that the technician charges for fixing the problem, which is $70 per hour.

Now, let's denote:
- \( y \) as the total cost,
- \( x \) as the number of hours spent fixing the problem.

The equation representing the total cost can therefore be expressed as:

\[
y = 70x + 50
\]

In this equation:
- \( 70 \) is the slope (rate of change), representing the cost per hour,
- \( 50 \) is the y-intercept (initial value), representing the initial diagnosis fee.

### Summary:
- **Initial value (b)**: $50 (the diagnosis fee)
- **Rate of change (m)**: $70 (the hourly rate)

Thus, the correct identification from the options you provided is:
**The initial value is $50 and the rate of change is $70.**