Question

What is the slope of the line parallel to points (0,2) (0,4)

a
-1/2

b
0

c
3/4

d
undefined

Answer 1

To find the slope of the line defined by the points (0, 2) and (0, 4), we start by identifying that both points have the same x-coordinate (0). This indicates that the line is vertical.

The formula for the slope \( m \) of a line between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

In this case, let \( (x_1, y_1) = (0, 2) \) and \( (x_2, y_2) = (0, 4) \). Substituting into the formula:

\[
m = \frac{4 - 2}{0 - 0} = \frac{2}{0}
\]

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

Since parallel lines have the same slope, the slope of any line parallel to this line (which is vertical) will also be undefined.

Therefore, the correct answer is:

d) undefined