What is the slope of the line that passes through the points left parenthesis, minus, 1, comma, minus, 7, right parenthesis(−1,−7) and left parenthesis, 1, comma, minus, 13, right parenthesis(1,−13)? Write your answer in simplest form.

To find the slope of the line passing through the points \((-1, -7)\) and \((1, -13)\), we use the slope formula:

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

Here, \((x_1, y_1)\) corresponds to the point \((-1, -7)\) and \((x_2, y_2)\) corresponds to the point \((1, -13)\).

Substituting these values into the slope formula:

\[
m = \frac{-13 - (-7)}{1 - (-1)}
\]

Simplify the expression:

\[
m = \frac{-13 + 7}{1 + 1} = \frac{-6}{2} = -3
\]

So, the slope of the line is \(\boxed{-3}\).

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

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Here are 8 related questions:

1. How do you find the slope if given two points in different quadrants?
2. What does the slope of a line represent geometrically?
3. How does changing one of the points affect the slope?
4. How do you interpret a positive vs. negative slope?
5. What is the slope-intercept form of a line, and how is the slope used in it?
6. How do you calculate the slope if the points are vertically aligned?
7. Can two different lines have the same slope? What does this imply?
8. How can you find the equation of the line after finding the slope?

**Tip:** Always double-check your points' coordinates when calculating the slope to avoid sign errors.

Learn how to find the slope of a line passing through the points (-1, -7) and (1, -13) using the slope formula. This problem involves basic analytic geometry concepts and is suitable for Grades 7-9 students.

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