Final answer:
The slope of a line perpendicular to the line with equation 6x + 5y = -30 is 5/6, which is the negative reciprocal of the original line's slope.
Step-by-step explanation:
To find the slope of the line perpendicular to the line represented by the equation 6x + 5y = -30, we need to manipulate the equation into slope-intercept form, which is y = mx + b, where m represents the slope, and b represents the y-intercept. First, let's solve for y:
- 6x + 5y = -30
- 5y = -6x - 30
- y = -(6/5)x - 6
The slope of this line is -6/5. The slope of a line perpendicular to this would be the negative reciprocal of -6/5, which is 5/6. Hence, the slope of the perpendicular line is 5/6.