To find the slope of a line that is perpendicular to another line, we can use the concept of negative reciprocals. When two lines are perpendicular, the slopes of those lines will multiply together to equal -1.
Given that the slope of the original line is 27, we can denote this slope as m. Therefore:
m = 27
To find the slope of the perpendicular line, we need to calculate the negative reciprocal of 27. This means we will flip the fraction and change the sign.
Since 27 can be expressed as a fraction:
27 = rac{27}{1}
The reciprocal of this fraction is:
rac{1}{27}
Now, we will change the sign to get the negative reciprocal:
Negative Reciprocal: – rac{1}{27}
Thus, the slope of the line that is perpendicular to the line with a slope of 27 is – rac{1}{27}.