## 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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