Final answer:
The slope of line e, which is perpendicular to line d with a slope of 5/7, is -7/5 as perpendicular lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
Given that line d has a slope of 5/7, and knowing that line e is perpendicular to line d, we can determine the slope of line e by utilizing the concept that the slopes of perpendicular lines are negative reciprocals of each other. In mathematics, particularly when dealing with the algebra of straight lines, this relationship is fundamental and applies to any linear equation represented on a Cartesian coordinate plane.
To find the slope of line e, we take the negative reciprocal of the slope of line d, which is 5/7. The reciprocal of 5/7 is 7/5, and therefore the negative reciprocal will be -7/5. Hence, the slope of line e, which is perpendicular to line d, is -7/5.