Find the slope of the line through P and Q.
P(2, −2), Q(8, −1)

The slope \( m \) of a line passing through two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is calculated using the formula:

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

Given:
- \( P(2, -2) \): \( x_1 = 2 \), \( y_1 = -2 \)
- \( Q(8, -1) \): \( x_2 = 8 \), \( y_2 = -1 \)

Substitute these values into the formula:

\[
m = \frac{-1 - (-2)}{8 - 2} = \frac{-1 + 2}{6} = \frac{1}{6}
\]

So, the slope of the line through points \( P \) and \( Q \) is:

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

Would you like further details or have any questions?

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1. How can you determine if two lines are parallel by comparing slopes?
2. What is the slope of a horizontal line?
3. How do you find the equation of a line given a point and the slope?
4. Can you find the midpoint between two points on a line?
5. How does the slope relate to the angle a line makes with the x-axis?

**Tip:** The slope of a line describes its steepness and direction. Positive slopes rise from left to right, while negative slopes fall.

Find the slope of the line through P and Q. P(2, −2), Q(8, −1)

Calculate the slope of the line passing through points P(2, -2) and Q(8, -1) using the slope formula. This solution includes step-by-step instructions suitable for students in Grades 8-10, covering key concepts in coordinate geometry.

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