https://file.aiquickdraw.com/mathbot/file/1726592811659l4vftpcn.jpg

To solve this, we need to find the equation of the line shown in the graph, which is typically in the form:

\[
\text{Cost} = m \times \text{mass of coal} + c
\]

Where:
- \( m \) is the gradient (slope) of the line.
- \( c \) is the y-intercept (where the line crosses the y-axis).

### Step 1: Find the Gradient (\(m\))
The gradient is calculated as the change in the y-values (Cost) divided by the change in the x-values (Mass of coal). From the graph:
- When the mass of coal is 0 tonnes, the cost is £0.
- When the mass of coal is 1 tonne, the cost is £200.

So, the gradient is:

\[
m = \frac{\text{Change in Cost}}{\text{Change in Mass}} = \frac{200 - 0}{1 - 0} = 200
\]

### Step 2: Find the Y-Intercept (\(c\))
From the graph, it's clear that the line passes through the origin (0, 0), meaning the y-intercept is \( c = 0 \).

### Final Formula
Thus, the formula for the cost based on the mass of coal is:

\[
\text{Cost} = 200 \times \text{mass of coal} + 0
\]

Or simply:

\[
\text{Cost} = 200 \times \text{mass of coal}
\]

Would you like more details on how this was derived, or do you have any other questions?

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Here are 5 related questions to further explore this topic:
1. How would the formula change if the graph had a different y-intercept?
2. What does the gradient of the line tell you about the cost per tonne of coal?
3. How would you calculate the cost for 1.5 tonnes of coal using this formula?
4. What would the graph look like if the cost started at £50 instead of £0?
5. How can you use this formula to predict the cost for a given mass of coal?

**Tip:** When interpreting graphs, always check if the line passes through the origin to simplify finding the equation.

Use the graph below to work out the values that complete the formula: Cost = ___ x mass of coal + ___

Learn how to derive the cost formula from a graph representing the cost of coal based on mass. This problem teaches how to calculate the gradient and intercept, suitable for students in Grades 7-9.

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