What is the slope of the line that passes through the points left parenthesis, minus, 5, comma, 8, right parenthesis(−5,8) and left parenthesis, minus, 5, comma, 4, right parenthesis(−5,4)

To find the slope of a line passing through two points, we use the formula:

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

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. 

Given the points \((-5, 8)\) and \((-5, 4)\):

- \((x_1, y_1) = (-5, 8)\)
- \((x_2, y_2) = (-5, 4)\)

Now, apply these values to the slope formula:

\[
m = \frac{4 - 8}{-5 - (-5)} = \frac{-4}{0}
\]

Since the denominator is 0, the slope is **undefined**. This indicates that the line is vertical.

### Summary:
- The slope of a line passing through the points \((-5, 8)\) and \((-5, 4)\) is **undefined**, as it is a vertical line.

Would you like more details, or do you have any questions?

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Here are some related questions for deeper exploration:

1. What is the equation of a vertical line?
2. How do we find the slope of a horizontal line?
3. What is the geometric interpretation of an undefined slope?
4. How can we determine if a line is vertical or horizontal using just the coordinates?
5. How is the slope of parallel and perpendicular lines calculated?

**Tip**: Vertical lines always have an undefined slope, and their equation is of the form \(x = a\), where \(a\) is the x-coordinate.

What is the slope of the line that passes through the points (−5,8) and (−5,4)?

Learn how to find the slope of the line passing through points (−5, 8) and (−5, 4). This problem explains how to use the slope formula and covers the concept of undefined slope for vertical lines. Suitable for students in Grades 7-10.

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