1. **State the problem:** We need to write an equation of the form $y = a \sin bx$ or $y = a \cos bx$ to describe the given sinusoidal graph. 2. **Identify key features from the graph:** - Amplitude $a = 4$ (the maximum value from the center line $y=0$). - Period $T = \frac{4\pi}{3}$. - The graph crosses the origin $(0,0)$ with a positive slope, indicating a sine function rather than cosine. 3. **Recall the formula for period:** $$T = \frac{2\pi}{b}$$ 4. **Solve for $b$ using the period:** $$b = \frac{2\pi}{T} = \frac{2\pi}{\frac{4\pi}{3}} = 2\pi \times \frac{3}{4\pi} = \frac{3}{2}$$ 5. **Write the equation:** Since the graph is sine with amplitude 4 and $b=\frac{3}{2}$, $$y = 4 \sin \left( \frac{3}{2} x \right)$$ 6. **Final answer:** $$\boxed{y = 4 \sin \left( \frac{3}{2} x \right)}$$