Find the slope of a line perpendicular to the line whose equation is 3, x, plus, 6, y, equals, minus, 543x+6y=−54. Fully simplify your answer.
First, we need to find the slope of the given line in slope-intercept form (y = mx + b):
Rearranging the given equation:
6y = -543x - 54
y = (-543/6)x - 54/6
y = -91x - 9
The slope of the given line is -91.
The slope of a line perpendicular to a line with slope m is the negative reciprocal of m. Therefore, the slope of a line perpendicular to the given line is:
m_perpendicular = -1 / m
m_perpendicular = -1 / (-91)
m_perpendicular = 1 / 91
Therefore, the slope of a line perpendicular to the given line is 1/91.