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 What is the slope of the line determined by any two solutions to the equation 4/x + 4/y = 0?

 Nov 13, 2020
 #1
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+1

Note  that  when  x = -4  and y = 4   the equation will be  true

 

And when x = 4  and y = -4  the equation will also be true

 

So.....the points  ( -4,4)  and ( 4,-4) will be  on the graph

 

The  slope is  [ -4-4 ] / [4 - -4 ]  = -8 / 8  =   -1

 

Algebraically....we can see that

 

x/4  + y/4  =  0

 

[4x + 4y] / [xy] = 0     multiply through by xy

 

4x + 4y  = 0     divide through by 4

 

x + y =  0   rearrange as

 

y =  -x

 

So...this confirms that the slope is -1

 

 

cool cool cool

 Nov 13, 2020

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