To find the equation in point slope form of the line passing through the points (2, 0) and (2, 8), we first need to determine the slope of the line.
The slope (m) is calculated using the formula:
m = (y2 – y1) / (x2 – x1)
Substituting our points (2, 0) as (x1, y1) and (2, 8) as (x2, y2):
m = (8 – 0) / (2 – 2) = 8 / 0
Since division by zero is undefined, we see that the slope is undefined. This indicates that the line is vertical.
The general form of a vertical line is x = a, where ‘a’ is the x-coordinate of any point on the line. In this case, both points have the x-coordinate of 2.
Thus, the equation of the line in this case is:
x = 2
Although this is not in point slope form, it correctly represents the vertical line that passes through the given points.