Find the slope of a line perpendicular to the line whose equation is x−3y=27. Fully simplify your answer.
To find the slope of the line perpendicular to the given line, we first need to find the slope of the given line.
To do this, we can rearrange the given equation into slope-intercept form, which is y = mx + b, where m is the slope:
x - 3y = 27
-3y = -x + 27
y = (1/3)x - 9
Comparing this equation with y = mx + b, we see that the slope (m) of the given line is 1/3.
The slope of a line perpendicular to a line with slope m is the negative reciprocal of m. So in this case, the slope of the line perpendicular to the given line is -(3/1), which simplifies to -3.
Therefore, the slope of the line perpendicular to the line x - 3y = 27 is -3.