To find the equation of the line passing through the points $(-2, 9)$ and $(1, -3)$, we will use the point-slope form of a line and follow these steps:

Step 1: Find the slope ($m$)

The slope is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the given points: $m = \frac{-3 - 9}{1 - (-2)} = \frac{-12}{1 + 2} = \frac{-12}{3} = -4$

Step 2: Use the point-slope form

The point-slope form of the equation of a line is: $y - y_1 = m(x - x_1)$ Using the point $(-2, 9)$ and $m = -4$: $y - 9 = -4(x - (-2))$ Simplify: $y - 9 = -4(x + 2)$ $y - 9 = -4x - 8$ $y = -4x + 1$

Final Answer:

The equation of the line is: $y = -4x + 1$

Would you like me to show more details or solve any related problems?

Here are 5 related questions for further practice:

1. What is the y-intercept of the line $y = -4x + 1$?
2. Find the x-intercept of the line $y = -4x + 1$.
3. Write the equation of a line parallel to $y = -4x + 1$ passing through $(2, 5)$.
4. Write the equation of a line perpendicular to $y = -4x + 1$ passing through $(-2, 9)$.
5. Verify whether the point $(0, 1)$ lies on the line $y = -4x + 1$.

Tip:

When working with linear equations, double-check slope calculations to ensure accurate results.