What is the equation of the line that passes through the origin and perpendicular to the line #x-3y =9#?

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Answer 1 · 2017-10-03T19:55:43

#y = -3x#

#x -3y = 9 => y= 1/3x-3#

If two lines are perpendicular the product of their gradients is:

#m_1 xx m_2 = -1#

so:

#1/3 xx m = -1 => m= -3#

If the line passes through the origin then:

#y = mx + b#

#0 = -3(0) + b=> b= 0#

So our equation is:

#y = -3x#

Graph of lines:

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