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What is the equation of the line perpendicular to #y=-2x # that passes through # (4,-1) #?

Answer 1

Genesis Allen

#" "color(green)(y=1/2x-3)#

Suppose the slope (gradient) of the original equation was m. Then we would have: #y=mx#

The line perpendicular would have the gradient of #(-1)xx1/m#

So for your equation #m=(-2)#

That means that the line perpendicular will have the gradient of

#(-1)xx 1/(-2)" "=" "+1/2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the new equation is: #y=1/2x#

The thing is that it should be #color(brown)(y=1/2x+c)#

where c is a constant value
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the value of c")#

We are given that #color(blue)((x,y)->(4,-1))#
So by substitution we have:

#" "color(brown)(color(blue)(-1) =1/2(color(blue)(4))+c#

#" "-1=2+c#

#" "c=-3# giving

#" "color(green)(y=1/2x-3)#

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Answer 2

Isaiah Anthony

The equation of the line perpendicular to ( y = -2x ) that passes through ( (4, -1) ) is ( y = \frac{1}{2}x - 3 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.