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What is the equation of the line perpendicular to #y = 1/2x + 1#?

Question

What is the equation of the line perpendicular to #y = 1/2x + 1#?
What is the equation of the line perpendicular to #y = 1/2x + 1#?

Answers

#y = -2x + c#, where #c# is any real constant.

Explanation:

The product of the gradients of 2 mutually perpendicular lines will be equal to #-1#.

Therefore, any line with gradient #frac{-1}{1/2} = -2# will be perpendicular to the line #y = 1/2 x + 1#.

The final answer is

#y = -2x + c#, where #c# is any real constant.

For a line to be perpendicular to another the product of their slopes must be #-1#, or #m_1xxm_2=-1#

Explanation:

The slope of the first line #m_1=+1/2#
The slope of the second line must then be #m_2=-2#
because their product is #-1#

Because we don't know anything else about the line, the answer is:
All lines of the form #g(x)=-2x+b#, where #b# can be any number.


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