Let’s solve the problem in the image together.

We are tasked with finding the slope of the line passing through the points $(1, -6)$ and $(-2, -8)$.

The slope formula is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the values:

• $x_1 = 1, y_1 = -6$
• $x_2 = -2, y_2 = -8$

$m = \frac{-8 - (-6)}{-2 - 1}$

Simplify the numerator and denominator:

$m = \frac{-8 + 6}{-2 - 1} = \frac{-2}{-3}$

Simplify further:

$m = \frac{2}{3}$

Final Answer:

The slope is $\frac{2}{3}$.

Would you like further clarification or additional examples?

Here are 5 related questions to explore further:

1. How do you find the slope of a vertical line?
2. What is the slope of a horizontal line?
3. How can you find the slope if one of the points is the origin?
4. What is the slope-intercept form of a line, and how is the slope used in it?
5. How do you interpret a negative slope on a graph?

Tip: Always double-check your subtraction when using the slope formula—small errors in signs can lead to incorrect answers!