Final answer:
The slope of the original line 3x + 18y = 108 is -1/6. The slope of a line perpendicular to this is the negative reciprocal, which is 6.
Step-by-step explanation:
To find the slope of a line perpendicular to the given line, we first need to identify the slope of the original line. The equation provided is 3x + 18y = 108, which can be rewritten in slope-intercept form (y = mx + b), where m represents the slope, and b represents the y-intercept.
First, we solve for y:
- 18y = -3x + 108
- y = (-3x/18) + (108/18)
- y = -1/6x + 6
The slope of the original line is -1/6. The slope of a line perpendicular to this would be the negative reciprocal. Therefore:
- The negative reciprocal of -1/6 is 6
The slope of a line perpendicular to the given line is 6.