Question: The points $(8, 3)$ and $(1, 6)$ 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. y-3=
1. **State the problem:** Find the equation of the line passing through the points $(8, 3)$ and $(1, 6)$ in point-slope form.
2. **Recall the point-slope form formula:**
$$y - y_1 = m(x - x_1)$$
where $m$ is the slope of the line and $(x_1, y_1)$ is a point on the line.
3. **Calculate the slope $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 3}{1 - 8} = \frac{3}{-7} = -\frac{3}{7}$$
4. **Choose one point to use in the equation:**
We use the point $(8, 3)$ as given in the prompt.
5. **Write the point-slope form equation:**
$$y - 3 = -\frac{3}{7}(x - 8)$$
6. **Final answer:**
The equation of the line in point-slope form is
$$\boxed{y - 3 = -\frac{3}{7}(x - 8)}$$