A student plots T² in s² against L in m for a simple pendulum…

Step 1. The slope. $m = \dfrac{3.85\ \text{s}^2 - 1.42\ \text{s}^2}{0.95\ \text{m} - 0.35\ \text{m}}$ $= \dfrac{2.43\ \text{s}^2}{0.60\ \text{m}}$ $= 4.05\ \text{s}^2/\text{m}$.

Step 2. The value of g. $g = \dfrac{4\pi^2}{m}$ $= \dfrac{39.48}{4.05\ \text{s}^2/\text{m}}$ $= 9.75\ \text{m/s}^2$.

Step 3. The error in the slope. $\Delta m = \dfrac{4.20 - 3.90}{2}\ \text{s}^2/\text{m}$ $= 0.15\ \text{s}^2/\text{m}$. The relative error is $\dfrac{0.15}{4.05} = 3.7\%$.

Step 4. The error in g. $g$ is in inverse proportion to the slope, so it has the same relative error. $\Delta g = 0.037 \times 9.75\ \text{m/s}^2$ $= 0.36\ \text{m/s}^2$.