What is the slope of the line that passes through the points left parenthesis, 0, comma, 0, right parenthesis(0,0) and left parenthesis, 0, comma, 5, right parenthesis(0,5)? Write your answer in *simplest form*.

To find the slope of the line passing through the points \((0, 0)\) and \((0, 5)\), we use the slope formula:

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

Here, \((x_1, y_1)\) corresponds to the point \((0, 0)\) and \((x_2, y_2)\) corresponds to the point \((0, 5)\).

Substituting these values into the slope formula:

\[
m = \frac{5 - 0}{0 - 0}
\]

However, the denominator becomes zero:

\[
m = \frac{5}{0}
\]

A fraction with a zero denominator is undefined, meaning the slope is **undefined**. This is because the line is vertical.

So, the slope of the line is \(\boxed{\text{undefined}}\).

Do you have any questions or would you like more details on this explanation?

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Here are 8 related questions:

1. What does it mean when a slope is undefined?
2. How do you graph a vertical line on the coordinate plane?
3. What is the slope of a horizontal line?
4. Can a line with an undefined slope be expressed in slope-intercept form?
5. How do you determine if a line is vertical just by looking at its equation?
6. What is the difference between an undefined slope and a zero slope?
7. How does the concept of slope apply to real-world scenarios, such as in construction?
8. What happens to the slope if the points are the same, for example, \((0, 0)\) and \((0, 0)\)?

**Tip:** Vertical lines have an undefined slope, while horizontal lines have a slope of zero.

Learn how to find the slope of a line passing through the points (0, 0) and (0, 5) using the slope formula. Understand why the slope is undefined for vertical lines. Suitable for students in Grades 7-9.

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