To find the equation of the line in slope-intercept form ($y = mx + b$), we need the slope ($m$) and the $y$-intercept ($b$).

Step 1: Calculate the slope ($m$)

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the given points $(2, -2)$ and $(3, -9)$: $m = \frac{-9 - (-2)}{3 - 2} = \frac{-9 + 2}{1} = \frac{-7}{1} = -7$

Step 2: Use the point-slope formula to find the equation

The point-slope form is: $y - y_1 = m(x - x_1)$ Substitute $m = -7$ and one of the points, say $(2, -2)$: $y - (-2) = -7(x - 2)$ Simplify: $y + 2 = -7x + 14$ $y = -7x + 12$

Final Answer:

The equation of the line in slope-intercept form is: $y = -7x + 12$

Would you like a detailed explanation of any step?

Here are 5 related questions for further exploration:

1. How do you find the equation of a line if only the slope and one point are given?
2. How can you verify if a point lies on a given line?
3. What is the slope-intercept form of a vertical line?
4. What happens to the slope when two points have the same $y$-coordinate?
5. How do you convert slope-intercept form to standard form?

Tip: When working with slopes, always subtract coordinates in the same order to avoid sign errors!