The problem describes a linear relationship between the total cost, $C$, and the number of minutes, $t$, spent using a computer at an internet cafe. Based on the graph, I can extract the following information:

1. Equation for $C$: The graph starts at $C = 9$ when $t = 0$, indicating that there is a fixed initial fee of $9$. As the number of minutes increases, the total cost $C$ increases linearly. From the graph, it appears that for every 5-minute increase, the cost increases by $5 (from $9 to $14 and $14 to $19).

   Thus, the equation of the line can be expressed as: $C = 9 + 1 \cdot t$ where $9$ is the initial cost, and $1$ is the slope (the cost per minute).

2. Slope of the Graph: The slope of the graph, $m$, is calculated as: $m = \frac{\text{Change in Cost}}{\text{Change in Time}} = \frac{14 - 9}{5 - 0} = 1$ This means that the cost increases by $1 for every additional minute used.

3. Interpretation of the Slope: The slope of the graph (1) represents the rate at which the total cost increases with each additional minute. In the context of the problem, it indicates that the internet cafe charges $1 per minute after the initial fee.

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Related Questions:

1. What would the total cost be if Arianys used the computer for 15 minutes?
2. How would the equation change if the initial fee increased by $3?
3. What is the significance of the y-intercept in the graph?
4. How can the equation be used to predict the cost for 30 minutes?
5. What would happen to the slope if the per-minute cost was reduced to $0.50?

Tip: To find the equation of a line given a graph, identify the y-intercept and calculate the slope using any two points on the line.