Final answer:
A line with an undefined slope that passes through (8,6) is a vertical line with the equation x = 8, which means all points on the line have an x-coordinate of 8.
Step-by-step explanation:
To prove that a line has an undefined slope and passes through the point (8,6), we need to understand what the characteristics of such a line are. An undefined slope indicates a vertical line, where all points on the line have the same x-coordinate. Since the line goes through the point (8,6), the line's equation is simply x = 8. This is because, on a vertical line, the x-value does not change, no matter what the y-value is. In summary, the equation of a line with an undefined slope passing through (8,6) is x = 8, and this line will be a straight line going up and down and intersecting the x-axis at x = 8.