In the xy-coordinate plane, the slope of line L is 3 and its y-intercept is 2. what is the equation of the line perpendicular to L that intersects L at its y- intercept?

1 Answer
smendyka
Feb 13, 2017

#y = color(red)(-1/3)x + color(blue)(2)#

Explanation:

First, we need to determine the slope of the line perpendicular to L. The slope of L, let's call it #m_L = 3#. The slope of a perpendicular line, let's call it #m_p# is the negative inverse of the slope of line L. Or, #m_p = -1/m_L#

#m_p = -1/3#

And, because the y-intercepts are the same we can use the slope-intercept to find the equation for the line in the problem:

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.

Substituting the slope we calculated and the y-intercept from the problem gives:

#y = color(red)(-1/3)x + color(blue)(2)#

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