What is the equation of a line that is perpendicular to #y=1/3x+9#?

Question

3599 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-08T14:31:21

#y = color(red)(-3)x + color(blue)(9)#

or

#y = color(red)(-3)x + color(blue)(b)# for any #color(blue)(b)# you choose.

This equation 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.

The equation is #y = color(red)(1/3)x + color(blue)(9)# therefore the slope of this line is #color(red)(m = 1/3)#.

A line perpendicular to this line will have a slope, let's call it #m_p#, which is the negative inverse of the slope of this line. Or, #m_p = -1/m#.

Substituting the slope of the line in the problem gives: #m_p = -3#

One equation of a line perpendicular to the line in the problem is:

#y = color(red)(-3)x + color(blue)(9)#

You can also pick any value for #b# to state the equation for a perpendicular line.