To find the equation in point-slope form of the line that passes through the points (2, 5) and (2, 3), we first need to determine the slope (m) of the line. The formula for calculating the slope between two points (x_1, y_1) and (x_2, y_2) is:
m = (y_2 - y_1) / (x_2 - x_1)
Substituting the coordinates of the given points, we have:
m = (3 - 5) / (2 - 2) = -2 / 0
Since the denominator is 0, this means that the slope is undefined and the line is vertical.
Vertical lines have equations in the form of x = a, where a is the x-coordinate through which the line passes. In this case, both points have the same x-coordinate of 2. Therefore, the equation of the line in point-slope form can be expressed as:
x = 2
It’s important to note that in the context of point-slope form, we typically use the formula:
y - y_1 = m(x - x_1)
However, since the slope is undefined, we cannot use this traditional format for vertical lines. Instead, we simply state the equation of the vertical line as x = 2.