1. **State the problem:** We need to find the equation that represents the water level $w$ after $d$ days based on the given data points: $(3, 96)$, $(6, 90)$, $(9, 84)$, $(12, 78)$, $(15, 72)$. 2. **Identify the pattern:** The water level decreases as days increase, suggesting a linear relationship of the form $$w = md + b$$ where $m$ is the slope and $b$ is the initial water level. 3. **Calculate the slope $m$:** Use two points, for example $(3, 96)$ and $(6, 90)$. $$m = \frac{90 - 96}{6 - 3} = \frac{-6}{3} = -2$$ 4. **Find the y-intercept $b$:** Use the point-slope form with point $(3, 96)$: $$96 = -2(3) + b$$ $$96 = -6 + b$$ $$b = 96 + 6 = 102$$ 5. **Write the equation:** $$w = -2d + 102$$ 6. **Check the options:** - A: $w = 2x + 102$ (incorrect slope sign) - B: $w = -102x + 2$ (incorrect slope and intercept) - C: $w = 102x - 2$ (incorrect slope and intercept) The correct equation is $w = -2d + 102$, which matches option A if $x$ is replaced by $d$ and the slope sign corrected. Since none exactly match, the closest correct form is option A with corrected slope sign. **Final answer:** $$w = -2d + 102$$