Final answer:
The equation of a line with an undefined slope that passes through the point (4,–3) is x = 4. This represents a vertical line where all points on the line have an x-coordinate of 4.
Step-by-step explanation:
The equation of a line with an undefined slope that passes through a specific point is a vertical line. This means that for every value of y, the x-coordinate remains constant. In this case, the line passes through the point (4,−3), so the equation of the line will simply be x = 4.
This equation indicates that the x-coordinate for all points on the line is 4, regardless of the y value, confirming that the slope is indeed undefined as the line is vertical and does not have a rate of change in the y direction.