How do you find the slope that is perpendicular to the line #4x-8y=-1#?

1 Answer
Euan S.
Jul 21, 2016

Slope is #-2#

Explanation:

Recall that we can perform operations on an equation as long as we do the same thing to both sides.

Add #8y# to both sides:

#4x = 8y - 1#

Add #1# to both sides:

#4x + 1 = 8y#

Divide both sides by 8:

#y = 1/2x +1/8#

This is now in standard form #y=mx+c# so we can read off that the slope of our original line is #1/2#.

Now, an important and useful fact is that the product of two perpendicular gradients is always equal to #-1#. This means that if we know a slope, we can work out a slope that will be perpendicular to it.

#m_1m_2 = -1#

#m_2 = -1/m_1#

#m_1 = 1/2 implies m_2 = -2#

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