Question: The points $(9, 3)$ and $(1, 1)$ fall on a particular line. What is its equation in point-slope form? Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
1. **State the problem:** Find the equation of the line passing through the points $(9, 3)$ and $(1, 1)$ in point-slope form.
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 $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{1 - 9} = \frac{-2}{-8}$$
4. **Simplify the slope:**
$$m = \frac{\cancel{-2}}{\cancel{-8}} = \frac{1}{4}$$
5. **Choose one point to use in the equation:** Let's use $(9, 3)$.
6. **Write the point-slope form equation:**
$$y - 3 = \frac{1}{4}(x - 9)$$
7. **Final answer:** The equation of the line in point-slope form is
$$y - 3 = \frac{1}{4}(x - 9)$$