To find the equation of a line that passes through two points, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let’s determine the slope (m) using the formula:
m = (y2 – y1) / (x2 – x1)
Here, our two points are (1, 5) and (1, 3):
- (x1, y1) = (1, 5)
- (x2, y2) = (1, 3)
Plugging these values into the slope formula gives:
m = (3 – 5) / (1 – 1)
This results in m = -2 / 0, which indicates that the slope is undefined. A line with an undefined slope is a vertical line.
Since both points have the same x-coordinate (1), the equation of the line can be expressed as:
x = 1
This means that for any value of y, the x-coordinate will always be 1, confirming that it is a vertical line passing through the points (1, 5) and (1, 3).