To find the equation of the line in point-slope form that passes through the points (2, 5) and (2, 3), we first need to determine the slope of the line.
The slope formula is given by:
m = (y2 – y1) / (x2 – x1)
Here, (x1, y1) = (2, 5) and (x2, y2) = (2, 3).
Substituting the values, we have:
m = (3 – 5) / (2 – 2) = -2 / 0
Since the denominator is zero, the slope is undefined, which tells us that this line is vertical.
The equation of a vertical line that passes through a specific x-coordinate can be expressed as:
x = a
In this case, since our points have an x-coordinate of 2, the equation of the line is:
x = 2
Since vertical lines don’t fit into the point-slope form (y – y1 = m(x – x1)), this is the simplest way to express it. Thus, the equation of the line passing through (2, 5) and (2, 3) is simply:
x = 2