Question: A line includes the points $(-2, 1)$ and $(-1, -8)$. 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 $(-2, 1)$ and $(-1, -8)$ 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 $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-8 - 1}{-1 - (-2)} = \frac{-9}{1} = -9$$
4. **Choose one point to use in the equation:** Let's use $(-2, 1)$.
5. **Write the point-slope form equation:**
$$y - 1 = -9(x - (-2))$$
which simplifies to
$$y - 1 = -9(x + 2)$$
6. **Final answer:**
$$\boxed{y - 1 = -9(x + 2)}$$
This is the equation of the line in point-slope form using integers and simplified fractions.