Solution:

We can determine the answers to the questions based on the graph. Here's how:

a) What is the cost of the connection fee?

The connection fee corresponds to the cost when the time $t = 0$ (i.e., the starting point on the vertical axis). From the graph:

• At $t = 0$, the cost $C = 200$ pence.

Thus, the connection fee is 200 pence.

b) What is the cost per minute?

The cost per minute can be calculated by finding the slope of the line, which is given by:

$\text{Slope} = \frac{\Delta C}{\Delta t}$

From the graph:

• At $t = 0$, $C = 200$ pence.
• At $t = 60$, $C = 600$ pence.

Substituting these values:

$\text{Slope} = \frac{600 - 200}{60 - 0} = \frac{400}{60} = 6.67 \, \text{pence per minute}.$

Thus, the cost per minute is 6.67 pence.

Final Answers:

1. Connection fee: 200 pence.
2. Cost per minute: 6.67 pence.

Would you like detailed steps or further clarification? Let me know!

Here are 5 follow-up questions to enhance understanding:

1. How would the graph look if the connection fee were reduced to 100 pence?
2. What happens to the slope if the cost per minute increases?
3. How would you write a formula to calculate the total cost $C(t)$ in terms of time $t$?
4. If the call lasted for 30 minutes, what would the total cost be?
5. What is the significance of the y-intercept in this type of graph?

Tip:

In linear graphs, the y-intercept always represents the fixed cost, and the slope gives the rate of change (e.g., cost per minute).