Final answer:
The slope of a line perpendicular to the line with the equation 4x - 5y = 10 is -5/4, as perpendicular slopes are negative reciprocals of each other.
Step-by-step explanation:
The slope of a line perpendicular to the line whose equation is 4x - 5y = 10 can be found by first expressing the given equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
To isolate the y-variable, we rearrange the equation to find y = (4/5)x - 2.
Therefore, the slope of the given line is 4/5. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of a line perpendicular to the given line would be the negative reciprocal of 4/5, which is -5/4.