1. **State the problem:** We have a straight line graph showing volume $V$ in litres over time $t$ in seconds. We need to find the gradient of the graph, explain what the gradient represents, and explain the meaning of the volume axis intercept. 2. **Formula for gradient:** The gradient $m$ of a straight line is given by $$m = \frac{\text{change in } y}{\text{change in } x} = \frac{\Delta V}{\Delta t}$$ where $\Delta V$ is the change in volume and $\Delta t$ is the change in time. 3. **Find the gradient:** From the graph, the line passes through points approximately $(0,4)$ and $(8,16)$. Calculate the change in volume: $$\Delta V = 16 - 4 = 12$$ Calculate the change in time: $$\Delta t = 8 - 0 = 8$$ Calculate the gradient: $$m = \frac{12}{8}$$ Show cancellation: $$m = \frac{\cancel{12}}{\cancel{8}} = \frac{3}{2} = 1.5$$ 4. **Interpret the gradient:** The gradient represents the rate of change of volume with respect to time. In other words, it tells us how many litres of liquid are added per second. 5. **Interpret the volume axis intercept:** The graph intersects the volume axis at $V=4$ when $t=0$. This means the container initially contains 4 litres of liquid before time starts. **Final answers:** - Gradient $= 1.5$ litres per second - Gradient represents the rate at which volume increases over time - Volume intercept represents the initial volume of liquid in the container