Try to find out what k is

Question

For what value of k will the graph of 6x+ky=6 Be perpendicular to the graph of 2x-6y=12

Answer 1

determine the slope of the first line (involves k); call it s

determine the slope of the other line; call that m.

 

m(s) = -1 when the two lines are ⊥

 

solve for k.

Answer 2

For what value of k will the graph of 6x+ky=6 Be perpendicular to the graph of 2x-6y=12

 

For two graphs or in this case lines to be perpendicular to each other, the product of their slopes should equal to -1

 

6x+ky=6 rewrite in terms of y, ky=-6x+6, y=-(6/k)x+(6/k) with -6/k

being the slope say m1=-6/k

 

For the 2nd equation 2x-6y=12, rearrange in terms of y

-6y=-2x+12, multiply by -1 you get 6y=2x-12. and y=(1/3)x-2

with 1/3 being the slope m2=1/3

 

Then m1m2=-1, (-6/k)(1/3)=-1 solve for k

 

-6/3k=-1, -6=-3k, k=2