https://file.aiquickdraw.com/mathbot/file/1727887065643910e4ut1.jpg

To determine the equation of the line shown in the graph for Andy's Appliance Repair, we can follow these steps:

### 1. Identify the points on the graph:
From the graph, we see that the line passes through the points:
- (0 hours, 0 dollars) — indicating no initial cost or flat fee.
- (3 hours, 200 dollars) — showing that for 3 hours of work, the cost is $200.

### 2. Calculate the slope:
The slope of the line $ m $ is given by the formula:

\[
m = \frac{{\text{{change in cost}}}}{{\text{{change in hours}}}} = \frac{200 - 0}{3 - 0} = \frac{200}{3} \approx 66.67
\]

This means the cost increases by about $66.67 for each hour worked.

### 3. Determine the equation:
Since the line passes through the origin (0, 0), the equation of the line is in the form:

\[
y = mx
\]

Substituting the slope $ m = \frac{200}{3} $, we get:

\[
\text{{Total Cost}} (y) = \frac{200}{3} \times \text{{Hours}} (x)
\]

Or:

\[
y = \frac{200}{3}x
\]

### Conclusion:
The equation for the graph is:

\[
y = \frac{200}{3}x
\]

Where:
- $ y $ represents the total cost.
- $ x $ represents the number of hours.

Let me know if you'd like further details or have any questions!

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Here are 5 related questions for further exploration:
1. How would the equation change if there was an initial service fee?
2. What would be the total cost for 5 hours of work based on this equation?
3. If a customer pays $400, how many hours of repair work were performed?
4. How would the slope change if the cost per hour increased to $80?
5. Can this type of graph be used for services with varying hourly rates?

**Tip:** In linear relationships, the slope represents the rate of change — in this case, the cost per hour.

Learn how to determine the equation of a linear graph for Andy's Appliance Repair service. The solution involves calculating the slope and writing the equation in slope-intercept form. The graph shows a total cost of $200 for 3 hours of work. Suitable for students in Grades 6-8.

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