1. **State the problem:** We are given a table showing the time $x$ in seconds and the distance $y$ a cheetah can sprint in feet. We need to find an equation that models the relationship between $x$ and $y$. 2. **Identify the type of relationship:** The distance increases as time increases, and the increments are consistent, suggesting a linear relationship of the form $$y = mx + b$$ where $m$ is the slope (rate of change) and $b$ is the y-intercept (distance at time zero). 3. **Calculate the slope $m$:** The slope is the change in distance divided by the change in time. Using the first two points $(5, 470)$ and $(10, 940)$: $$m = \frac{940 - 470}{10 - 5} = \frac{470}{5} = 94$$ 4. **Find the y-intercept $b$:** Use the equation $y = mx + b$ with one point, for example $(5, 470)$: $$470 = 94 \times 5 + b$$ $$470 = 470 + b$$ $$b = 470 - 470 = 0$$ 5. **Write the equation:** The linear model is $$y = 94x + 0$$ or simply $$y = 94x$$ 6. **Interpretation:** This means the cheetah runs 94 feet every second, starting from 0 feet at time 0 seconds. **Final answer:** $$y = 94x$$