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

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 $t = 0$).

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.

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.

4. Writing the equation:

Now that we know the slope is $1$ and the y-intercept is $9$, the equation becomes:

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

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.

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

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?

Tip:

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