1. **State the problem:** We need to find an equation of the form $y = a \sin(x)$ for a sinusoidal graph with maximum near 3.5 and minimum near -3.5. 2. **Recall the formula:** The general sine function is $y = a \sin(x)$ where $a$ is the amplitude. 3. **Important rule:** The amplitude $a$ is half the distance between the maximum and minimum values of the sine wave. 4. **Calculate amplitude:** $$a = \frac{\text{max} - \text{min}}{2} = \frac{3.5 - (-3.5)}{2} = \frac{7}{2} = 3.5$$ 5. **Write the equation:** $$y = 3.5 \sin(x)$$ 6. **Interpretation:** The sine wave oscillates between $-3.5$ and $3.5$ centered at $y=0$, matching the graph described. **Final answer:** $$y = 3.5 \sin(x)$$