Final answer:
The slope of a line perpendicular to the line through (0,3) and (4,3) is undefined because the given line is horizontal with a slope of 0, and the perpendicular line to a horizontal line is vertical.
Step-by-step explanation:
To find the slope of a line perpendicular to the line through (0,3) and (4,3), we first need to determine the slope of the given line. Since the y-coordinates of both points are the same, the line is horizontal and the slope is 0. A line that is perpendicular to a horizontal line is a vertical line, which has an undefined slope. However, in terms of finding a slope value that can be used in slope-intercept form (y = mx + b), perpendicular slopes are negative reciprocals of each other. In this case, the negative reciprocal of 0 is undefined, but since we often describe the slope of a vertical line as such, the concept of slope doesn't strictly apply. Thus, a line perpendicular to a horizontal line does not have a slope that can be quantified in a number, it is considered to have an undefined slope.