To find the equation of the line that passes through the points $(-1, 4)$ and $(2, -5)$, follow these steps:

Step 1: Find the slope ($m$)

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the given points $(-1, 4)$ and $(2, -5)$: $m = \frac{-5 - 4}{2 - (-1)} = \frac{-9}{3} = -3$

Step 2: Use the point-slope form

The point-slope form of the equation of a line is: $y - y_1 = m(x - x_1)$

Choose one of the points (e.g., $(-1, 4)$) and substitute $m = -3$, $x_1 = -1$, and $y_1 = 4$: $y - 4 = -3(x - (-1))$

Simplify: $y - 4 = -3(x + 1)$ $y - 4 = -3x - 3$ $y = -3x + 1$

Final Equation

The equation of the line is: $y = -3x + 1$

Would you like to see a graph or more details? Here are some related questions to expand your understanding:

1. How do you find the slope when given two points with the same $x$-coordinate?
2. What happens to the equation of a line if the slope is zero?
3. How do you rewrite the equation $y = -3x + 1$ in standard form?
4. What is the significance of the y-intercept in the line's equation?
5. Can you find the midpoint of the segment joining the two points $(-1, 4)$ and $(2, -5)$?

Tip: Always verify your calculations by substituting the given points back into the final equation.