Subjects algebra

Line Gradient 3D443B

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Line Gradient 3D443B


1. **Problem statement:** We have a straight line graph showing the cost (£) against units used. The line passes through points (0,0) and (100,10). 2. **Formula for gradient:** The gradient $m$ of a straight line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the gradient:** Using points $(0,0)$ and $(100,10)$: $$m = \frac{10 - 0}{100 - 0} = \frac{10}{100} = 0.1$$ 4. **Interpretation of the gradient:** The gradient represents the change in cost per unit increase in units used. So, it is the cost per unit of gas. 5. **Answer to part b:** The correct statement is **C - The cost per unit of gas.**