What is the slope of the line that passes through the points left parenthesis, minus, 8, comma, minus, 1, right parenthesis(−8,−1) and left parenthesis, minus, 8, comma, minus, 11, right parenthesis(−8,−11)? Write your answer in simplest form.

To find the slope of the line passing through two points, \((x_1, y_1)\) and \((x_2, y_2)\), you use the slope formula:

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

Given the points \((-8, -1)\) and \((-8, -11)\), let's plug these into the formula:

\[
\text{slope} = \frac{-11 - (-1)}{-8 - (-8)} = \frac{-11 + 1}{-8 + 8} = \frac{-10}{0}
\]

The denominator is \(0\), which means the slope is undefined. 

This indicates that the line is vertical, as all vertical lines have an undefined slope.

**Final answer**: The slope is undefined.

Would you like any additional details or have further questions on this topic?

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Here are 5 related questions you might find interesting:
1. What is the equation of the line with an undefined slope that passes through \((-8, -1)\)?
2. How do you find the slope of a horizontal line?
3. What does it mean geometrically when the slope is undefined?
4. How can you determine if two lines are parallel by comparing their slopes?
5. What is the slope of the line through the points \((3, 7)\) and \((6, 10)\)?

**Tip:** A vertical line has an equation of the form \(x = \text{constant}\), and its slope is always undefined.

What is the slope of the line that passes through the points (−8,−1) and (−8,−11)? Write your answer in simplest form.

Learn how to determine the slope of a line passing through the points (−8,−1) and (−8,−11). Understand why the slope is undefined due to the line being vertical. This problem is ideal for students in Grades 8-10 studying coordinate geometry and algebra.

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