Find the slope between the points  (4,0)and (4,4) Enter DNE if the slope between the points is undefined.

To find the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula:

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

For the points \((4, 0)\) and \((4, 4)\):
- \(x_1 = 4\), \(y_1 = 0\)
- \(x_2 = 4\), \(y_2 = 4\)

Substitute into the formula:

\[
\text{slope} = \frac{4 - 0}{4 - 4} = \frac{4}{0}
\]

Since division by zero is undefined, the slope does not exist. So, we enter:

\[
\text{DNE}
\]

This means the line is vertical, which does not have a defined slope.

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

Here are some related questions:
1. What is the slope of a horizontal line?
2. How do we determine if a line is vertical or horizontal based on two points?
3. Can a slope be negative, and what does that represent geometrically?
4. How do slopes relate to the angles of lines?
5. How do we calculate the slope of a line in three-dimensional space?

**Tip:** If two points have the same \( x \)-coordinate, the line between them is vertical, leading to an undefined slope.

Find the slope between the points (4,0) and (4,4). Enter DNE if the slope between the points is undefined.

Learn how to find the slope between the points (4,0) and (4,4) using the slope formula. This example demonstrates why the slope is undefined for vertical lines, providing insights into coordinate geometry and linear equations. Suitable for students in Grades 6-8.

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