Question: A line includes the points $(5, 10)$ and $(4, 2)$. 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 $(5, 10)$ and $(4, 2)$ in point-slope form.
2. **Recall the formula for point-slope form:**
$$y - y_1 = m(x - x_1)$$
where $m$ is the slope of the line and $(x_1, y_1)$ is a point on the line.
3. **Calculate the slope $m$ using the two points:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 10}{4 - 5} = \frac{-8}{-1} = 8$$
4. **Choose one of the points to use in the equation.** Let's use $(5, 10)$.
5. **Substitute $m = 8$ and $(x_1, y_1) = (5, 10)$ into the point-slope formula:**
$$y - 10 = 8(x - 5)$$
6. **This is the equation of the line in point-slope form.**
**Final answer:**
$$y - 10 = 8(x - 5)$$