Question: The graph shows the cost of different masses of lemons.
cost ($)
mass (kg)
0,0 to 5,14.5 line graph in the top-right.
Work out the cost of 6 kg of lemons.
1. **State the problem:** We need to find the cost of 6 kg of lemons given a linear relationship between mass and cost shown by the graph from (0,0) to (5,14.5).
2. **Identify the formula:** Since the graph is a straight line through the origin, the cost $C$ is proportional to the mass $m$. The formula is:
$$C = km$$
where $k$ is the constant of proportionality (cost per kg).
3. **Find the constant $k$:** Using the point $(5,14.5)$,
$$k = \frac{C}{m} = \frac{14.5}{5} = 2.9$$
So, the cost per kg is $2.9$.
4. **Calculate the cost for 6 kg:**
$$C = 2.9 \times 6 = 17.4$$
5. **Answer:** The cost of 6 kg of lemons is **17.4**.