use the point slope formula to find the slope of the line between the given points (-4,1) and (2,-5)

To find the slope between two points \((-4,1)\) and \( (2,-5) \) using the point-slope formula, we start by recalling the formula for the slope \(m\) between two points:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

### Step 1: Substitute the coordinates
Given:
- \((x_1, y_1) = (-4, 1)\)
- \((x_2, y_2) = (2, -5)\)

Substitute these values into the formula:

\[
m = \frac{-5 - 1}{2 - (-4)}
\]

### Step 2: Simplify the expression
Calculate the differences in the numerator and the denominator:

\[
m = \frac{-6}{6} = -1
\]

### Answer:
The slope \(m\) of the line between the points \((-4,1)\) and \( (2,-5) \) is:

\[
m = -1
\]

Would you like more details on how to apply this formula? 

Here are 5 related questions:
1. How would you find the equation of the line given these points?
2. What does the slope of \(-1\) indicate about the line's direction?
3. How can you verify the slope by graphing these points?
4. What if one point was different, say, \((2, -3)\) instead of \((2, -5)\)?
5. How does the slope formula apply if both points have the same \(x\)-coordinate?

**Tip:** When finding the slope, pay close attention to the signs in each coordinate to avoid errors!

Learn how to find the slope of a line between the points (-4,1) and (2,-5) using the point-slope formula. This detailed step-by-step guide covers algebraic concepts such as the slope formula, making it ideal for students in Grades 8-10.

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