Understanding the Point-Slope Form
The point-slope form of a line is given by the equation:
y – y1 = m(x – x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Finding the Slope (m)
The slope (m) between two points (x1, y1) and (x2, y2) is calculated as follows:
m = (y2 – y1) / (x2 – x1)
For the points (2, 0) and (2, 8):
- (x1, y1) = (2, 0)
- (x2, y2) = (2, 8)
Substituting the values:
m = (8 – 0) / (2 – 2)
This gives us:
m = 8 / 0
Since division by zero is undefined, the slope is undefined. This implies that the line is vertical.
Writing the Equation
x = 2
Thus, the equation of the line passing through the points (2, 0) and (2, 8) in point-slope form is:
y = m(x – 2), where m is undefined.
Conclusion
In summary, the vertical line through these points can be expressed simply as x = 2, since it doesn’t adhere to the typical point-slope equation due to its vertical nature.