Question

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

Answer 1

To find the slope of a line that passes through two points, we use the formula for slope \( m \):

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

In this case, the points given are \( (1, -7) \) and \( (1, 13) \).

Assigning the coordinates:

- \( (x_1, y_1) = (1, -7) \)
- \( (x_2, y_2) = (1, 13) \)

Now, we can substitute the coordinates into the slope formula:

\[
m = \frac{13 - (-7)}{1 - 1}
\]
\[
m = \frac{13 + 7}{1 - 1}
\]
\[
m = \frac{20}{0}
\]

Since division by zero is undefined, this means that the slope of the line is undefined.

Thus, the line is vertical because both points have the same x-coordinate.

The answer is that the slope is **undefined**.