1. **State the problem:** Find the equation of the line in point-slope form passing through the points $(9, -\frac{1}{2})$ and $(7, \frac{3}{2})$. 2. **Recall the formula:** The point-slope form of a line is given by: $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\frac{3}{2} - \left(-\frac{1}{2}\right)}{7 - 9} = \frac{\frac{3}{2} + \frac{1}{2}}{-2} = \frac{\frac{4}{2}}{-2} = \frac{2}{-2} = -1$$ 4. **Write the equation using point-slope form:** Choose point $(9, -\frac{1}{2})$: $$y - \left(-\frac{1}{2}\right) = -1(x - 9)$$ 5. **Simplify the equation:** $$y + \frac{1}{2} = -1(x - 9)$$ 6. **Final answer:** $$y + \frac{1}{2} = -1(x - 9)$$ This is the equation of the line in point-slope form with integers in the slope and point coordinates as required.