1. **State the problem:** We are given a set of time and distance data points and told the relationship is linear. We want to find the linear equation relating distance $d$ (km) to time $t$ (hours). 2. **Formula for linear relation:** The general form is $$d = mt + b$$ where $m$ is the slope (rate of change) and $b$ is the y-intercept (distance at time zero). 3. **Calculate the slope $m$:** Choose two points, for example $(t_1, d_1) = (0.5, 45)$ and $(t_2, d_2) = (1.5, 135)$. $$m = \frac{d_2 - d_1}{t_2 - t_1} = \frac{135 - 45}{1.5 - 0.5} = \frac{90}{1} = 90$$ 4. **Find the intercept $b$:** Use one point and the slope in the equation $d = mt + b$. Using $(0.5, 45)$: $$45 = 90 \times 0.5 + b$$ $$45 = 45 + b$$ $$b = 45 - 45 = 0$$ 5. **Write the final equation:** $$d = 90t + 0$$ or simply $$d = 90t$$ 6. **Interpretation:** The distance increases by 90 km every hour, starting from zero at time zero. This matches all given data points, confirming the linear relation.