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The graph shows the relationship between the cost and the mass of coal in tonnes. The formula you're asked to complete is of the form:

\[
\text{Cost} = m \times \text{Mass of Coal} + b
\]

Where:
- \( m \) is the slope of the line (rate at which the cost increases with mass).
- \( b \) is the y-intercept (the initial cost when the mass of coal is 0).

### Step 1: Determine the slope \( m \)

The slope \( m \) can be calculated using the formula:

\[
m = \frac{\Delta y}{\Delta x} = \frac{\text{Change in Cost}}{\text{Change in Mass of Coal}}
\]

From the graph, we can pick two points:
- At mass of coal = 0, the cost = 0 (point (0,0)).
- At mass of coal = 2 tonnes, the cost = 400 pounds (point (2, 400)).

Thus, the slope \( m \) is:

\[
m = \frac{400 - 0}{2 - 0} = \frac{400}{2} = 200
\]

### Step 2: Determine the intercept \( b \)

From the graph, it's clear that the line passes through the origin (0,0), meaning that the y-intercept \( b \) is 0.

### Final Formula

Now that we have both \( m = 200 \) and \( b = 0 \), the formula becomes:

\[
\text{Cost} = 200 \times \text{Mass of Coal}
\]

Let me know if you'd like more details or have any questions. Here are some related questions to expand on the topic:

1. How would the formula change if there were a fixed cost regardless of the amount of coal purchased?
2. Can you explain why the slope represents the rate of change in cost per tonne of coal?
3. What if the graph showed a steeper line? How would that affect the cost per tonne?
4. How can we interpret the graph if the cost starts at a higher value, meaning \( b \) is not 0?
5. How could you apply this formula in a real-world scenario where transportation costs are added?

**Tip**: Always check the scale of the axes when interpreting graphs, as different scales can affect how you interpret the slope and intercept.

Use the graph below to work out the values that complete the formula for cost against the mass of coal.

Learn how to calculate the cost of coal based on its mass using a linear graph. This problem covers key mathematical concepts like slope, intercept, and graph interpretation, perfect for students in Grades 7-9.

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