What is the slope of the line perpendicular to # y=2/3x-6 #?

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Answer 1 · 2017-08-19T21:05:40

Slope of the line perpendicular to #y# is #-3/2#
See a solution process below:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

#y = color(red)(2/3)x - color(blue)(6)#

Therefore, the slope of the line represented by the equation in the problem is:

#color(red)(m = 2/3)#

Let's call the slope of a perpendicular line: #m_p#

The slope of a perpendicular line is:

#m_p = -1/m#

Substituting gives:

#m_p = -1/(2/3) = -3/2#