1. **State the problem:** We need to write a linear equation that models the amount of flour $y$ in grams in the machine as a function of time $x$ in minutes since the machine was turned on. 2. **Identify given points:** From the graph, the machine starts with 800 grams of flour at time $x=0$, so the point is $(0, 800)$. 3. The machine empties after 4 minutes, so the flour amount is 0 grams at $x=4$, giving the point $(4, 0)$. 4. **Find the slope $m$ of the line:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 800}{4 - 0} = \frac{-800}{4} = -200$$ 5. **Use the slope-intercept form $y = mx + b$:** We know $m = -200$ and the y-intercept $b$ is the amount of flour at $x=0$, which is 800. 6. **Write the equation:** $$y = -200x + 800$$ 7. **Interpretation:** This means the machine loses 200 grams of flour every minute until it is empty at 4 minutes. **Final answer:** $$y = -200x + 800$$