1. **State the problem:** We are given the slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ as $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ and we need to solve for $y_2$. 2. **Recall the formula:** The slope $m$ is the ratio of the change in $y$ to the change in $x$ between two points. 3. **Isolate $y_2$:** Multiply both sides of the equation by $(x_2 - x_1)$ to get rid of the denominator: $$m(x_2 - x_1) = y_2 - y_1$$ 4. **Solve for $y_2$:** Add $y_1$ to both sides: $$y_2 = m(x_2 - x_1) + y_1$$ 5. **Interpretation:** This formula allows you to find the $y$-coordinate of the second point if you know the slope $m$, the $x$-coordinates $x_1$ and $x_2$, and the $y$-coordinate $y_1$ of the first point. **Final answer:** $$y_2 = m(x_2 - x_1) + y_1$$