To find the point through which the line passes, we need to consider the equation of the line that is perpendicular to the line with equation y = -1.
The equation y = -1 represents a horizontal line parallel to the x-axis. A line perpendicular to this line would be a vertical line parallel to the y-axis. Since it passes through the point (2,3), it means the x-coordinate remains the same for this perpendicular line.
Therefore, the line passing through (2,3) and perpendicular to the line y = -1 would have the equation x = 2.
To determine which point the line also passes through, we can substitute x = 2 into the given options:
For (1,4):
When x = 2, the y-coordinate is not 4, so (1,4) is not on the line x = 2.
For (2,-4):
When x = 2, the y-coordinate is not -4, so (2,-4) is not on the line x = 2.
For (-2,3):
When x = 2, the y-coordinate remains 3, so (-2,3) is on the line x = 2.
Therefore, the graph of the line through (2,3) that is perpendicular to the line with equation y = -1 also goes through the point (-2,3).