Find the slope of a line perpendicular to the line whose equation is 27x−3y=27. Fully simplify your answer.
To find the slope of a line perpendicular to a given line, we can find the slope of the given line and then take the negative reciprocal.
First, let's rewrite the equation of the given line in slope-intercept form:
27x - 3y = 27
-3y = -27x + 27
y = 9x - 9
The equation is now in the form y = mx + b, where m represents the slope. In this case, the slope is 9.
The negative reciprocal of 9 is -1/9.
Therefore, the slope of a line perpendicular to the line whose equation is 27x - 3y = 27 is -1/9.