https://file.aiquickdraw.com/mathbot/file/1730051077548eavn7d01.jpg

From the image, we can interpret the graph of \( C \) and use it to answer the question step by step.

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### 1. **Setting up the equation:**
The total cost \( C \) is modeled as a **linear equation** since the graph shows a straight line. A linear equation generally takes the form:

\[
C(t) = mt + b
\]

where:
- \( m \) is the **slope** (representing the rate of change or the cost per minute).
- \( b \) is the **y-intercept** (representing the initial fee, or the cost when \( t = 0 \)).

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### 2. **Extracting points from the graph:**
From the graph, we can identify two points on the line:
- \( (0, 9) \) — meaning the initial fee is 9 dollars.
- \( (5, 14) \) — meaning the total cost is 14 dollars after 5 minutes.

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### 3. **Finding the slope \( m \):**
The slope \( m \) measures the rate of change in cost per minute. We use the formula for slope:

\[
m = \frac{C_2 - C_1}{t_2 - t_1}
\]

Using the points \( (0, 9) \) and \( (5, 14) \):

\[
m = \frac{14 - 9}{5 - 0} = \frac{5}{5} = 1
\]

Thus, the slope is \( 1 \). This means the cost increases by **1 dollar per minute**.

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### 4. **Writing the equation:**
Now that we know the slope is \( 1 \) and the y-intercept is \( 9 \), the equation becomes:

\[
C(t) = 1 \cdot t + 9 \quad \text{or simply} \quad C(t) = t + 9
\]

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### 5. **Interpreting the slope:**
The slope of 1 represents the **additional cost per minute** of using the computer at the internet café. For every extra minute spent, the total cost increases by 1 dollar.

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Let me know if you want further details or have additional questions! 

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### 5 Related Questions:
1. What would the equation be if the slope were 2 instead of 1?
2. How would the graph change if the initial fee were lowered to 5 dollars?
3. If Aranys spends 10 minutes using the computer, what will be the total cost?
4. How does changing the y-intercept affect the total cost equation?
5. What happens to the slope if the price per minute doubles?

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### Tip:
In linear equations, always look for the slope and y-intercept first, as they provide the most important information for graph interpretation.

Aranys is going to use a computer at an internet café. The café charges an initial fee to use the computer and then an additional price per minute of usage. Let C represent the total cost of using a computer for t minutes at the internet café. A graph of C is shown below. Write an equation for C then state the slope of the graph and determine its interpretation in the context of the problem.

Learn how to determine the linear equation and interpret the slope for the total cost of using a computer at an internet café. Understand the concept of slope as the cost per minute and the y-intercept as the initial fee. Suitable for Grade 8 students.

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