To solve this problem, we use the point-slope form of a linear equation:

$y - y_1 = m(x - x_1),$

where $m$ is the slope, and $(x_1, y_1)$ is the point the line passes through. Substituting the given slope $m = -\frac{5}{2}$ and the point $(4, -9)$, the equation becomes:

$y - (-9) = -\frac{5}{2}(x - 4).$

Simplify this step by step:

1. Expand $y - (-9)$ to $y + 9$: $y + 9 = -\frac{5}{2}(x - 4).$

2. Distribute $-\frac{5}{2}$ to $x - 4$: $y + 9 = -\frac{5}{2}x + 10.$

3. Isolate $y$ to write the equation in slope-intercept form ($y = mx + b$): $y = -\frac{5}{2}x + 10 - 9.$

4. Simplify the constant: $y = -\frac{5}{2}x + 1.$

The equation in slope-intercept form is:

$\boxed{y = -\frac{5}{2}x + 1}.$

Would you like further explanation or practice with similar problems? Here are five follow-up questions:

1. How would you graph the line $y = -\frac{5}{2}x + 1$ on a coordinate plane?
2. What is the $y$-intercept of the line, and how do you find it from the equation?
3. How can you verify that the point $(4, -9)$ lies on this line?
4. What happens to the equation if the slope changes to $-\frac{3}{2}$?
5. Can you convert the equation into standard form ($Ax + By = C$)?

Tip:

When converting between forms of linear equations, always keep the slope and a known point consistent to avoid errors.