Draw a graph and explain the relationship between minutes used and total cost based on the provided data.

A graph showing the relationship between minutes and total cost would have the following characteristics:

• Title: Relationship between Minutes and Total Cost
• X-axis label: Minutes (m)
• Y-axis label: Total Cost (R)
• Scale: A suitable scale would be 5 units per major grid line on the x-axis (for minutes) and 10 or 20 units per major grid line on the y-axis (for cost).
• Plotted points: At least five points from the table (0,0), (5, 12.50), (10, 25.00), (15, 37.50), (20, 50.00), (30, 75.00) would be plotted.
• Line: A straight line would be drawn connecting these points, starting from the origin (0,0).

The type of relationship shown is a linear relationship or direct proportion.

The value at $m=0$ represents the initial cost or the cost when no minutes are used, which is R0.

The gradient represents the cost per minute. In this case, it is R2.50 per minute.

Yes, the graph passes through the origin.
This is because when $m=0$ minutes are used, the total cost $C = 2.50 \times 0 = 0$. So, the point $(0,0)$ is on the graph.

Yes, this relation is a function.
For every input value of minutes ($m$), there is exactly one output value for the total cost ($C$). It satisfies the vertical line test.

The formula for the total cost is $C = 2.50m$.

• For 25 minutes: $$C = 2.50 \times 25$$ $$C = 62.50$$ The cost for 25 minutes is R62.50.
• For 60 minutes: $$C = 2.50 \times 60$$ $$C = 150.00$$ The cost for 60 minutes is R150.00.

If a person spends R100, we need to find the number of minutes ($m$).

If a person spends R100, they use 40 minutes.

For another company, the charges are R10 fixed fee and R3 per minute.
Let $C'$ be the total cost for this company and $m$ be the number of minutes.
The formula for the total cost is: