To determine the equation of a line that passes through the point (2, 1) with an undefined slope, we need to understand what an undefined slope represents. An undefined slope occurs when a line is vertical. This means that all points on the line have the same x-coordinate.
In this scenario, since the line passes through the point (2, 1), the x-coordinate of every point on this vertical line will be exactly 2. Therefore, the equation of the line can be expressed in the form:
x = aSubstituting the value from our given point, the equation becomes:
x = 2This equation indicates that regardless of the value of y, the x-coordinate will always be 2. Hence, the line runs vertically through the point (2, 1) and extends infinitely in the upward and downward directions.