Final answer:
The slope of the given line 8x + 10y = 60 is -4/5. The slope of a line perpendicular to this is the negative reciprocal, which is 5/4.
Step-by-step explanation:
To find the slope of a line perpendicular to the line whose equation is 8x + 10y = 60, we first need to rewrite the given equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, we solve for y:
- 8x + 10y = 60
- 10y = -8x + 60
- y = -(4/5)x + 6
The slope of the original line is -4/5. Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of a line perpendicular to the given line is 5/4.