1. **Stating the problem:** We are given a table of height $y$ in meters versus time $x$ in seconds: $$\begin{array}{c|c} \text{Time }(s) & \text{Height }(m) \\ \hline 0 & 360 \\ 10 & 300 \\ 20 & 240 \\ 30 & 180 \\ 40 & 120 \end{array}$$ We want to find the relationship between height and time, assuming a linear model, and solve for the equation of the line $y=f(x)$. 2. **Formula and rules:** For a linear relationship, the equation is: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. The slope $m$ is calculated by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** Using the first two points $(0,360)$ and $(10,300)$: $$m = \frac{300 - 360}{10 - 0} = \frac{-60}{10} = -6$$ 4. **Find the y-intercept $b$:** Since at $x=0$, $y=360$, the intercept is: $$b = 360$$ 5. **Write the equation:** $$y = -6x + 360$$ 6. **Interpretation:** This means the height decreases by 6 meters every second. 7. **Verification:** Check with another point, say $(20,240)$: $$y = -6(20) + 360 = -120 + 360 = 240$$ which matches the table. **Final answer:** $$\boxed{y = -6x + 360}$$ This is the height as a function of time.