1. **Stating the problem:** We are given a graph with a red ascending line labeled $S_1$ representing the supply curve for wireless earbuds. The line starts near quantity 2 with price 1 and goes up to quantity 8 with price 9. There is a point $A_1$ at quantity 4 and price 5, where two dotted lines intersect. 2. **Understanding the supply curve:** The supply curve $S_1$ is a straight line, so it can be represented by a linear equation of the form $$p = m q + b$$ where $p$ is the price per unit, $q$ is the quantity, $m$ is the slope, and $b$ is the y-intercept. 3. **Finding the slope $m$:** Using the two points on the supply line: $(q_1, p_1) = (2,1)$ and $(q_2, p_2) = (8,9)$, the slope is $$m = \frac{p_2 - p_1}{q_2 - q_1} = \frac{9 - 1}{8 - 2} = \frac{8}{6} = \frac{4}{3}.$$ 4. **Finding the y-intercept $b$:** Use point $(2,1)$ in the equation $p = m q + b$: $$1 = \frac{4}{3} \times 2 + b \implies 1 = \frac{8}{3} + b \implies b = 1 - \frac{8}{3} = \frac{3}{3} - \frac{8}{3} = -\frac{5}{3}.$$ 5. **Equation of the supply curve $S_1$:** $$p = \frac{4}{3} q - \frac{5}{3}.$$ 6. **Check point $A_1$ at $(4,5)$:** Substitute $q=4$: $$p = \frac{4}{3} \times 4 - \frac{5}{3} = \frac{16}{3} - \frac{5}{3} = \frac{11}{3} \approx 3.67,$$ which is not equal to 5, so $A_1$ is not on the supply curve but is a reference point. 7. **Summary:** The supply curve $S_1$ is given by $$\boxed{p = \frac{4}{3} q - \frac{5}{3}}.$$