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anonymous
 one year ago
For what value of k are the two lines 2x +ky =3 and x+y=1
(a)parallel?
(b)perpendicular?
anonymous
 one year ago
For what value of k are the two lines 2x +ky =3 and x+y=1 (a)parallel? (b)perpendicular?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if two lines are parallel, that means their "slope" is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right so.... let us put those two fellows in slopeintercept form so \(\bf \begin{cases} 2x+ky=3\to ky=2x+3\to y=\cfrac{2x+3}{k}\to &y=\cfrac{2}{k}+\cfrac{3}{k} \\ \quad \\ x+y=1\to y=x+1\to &y=1x+1 \end{cases}\) notice the slopes of each of them

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah the slop of the first one is 2/k and the second one is 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the 1st one has a slope of 2/k the 2nd one, has a slope of 1 what should "k" need to be, for them to be equal? well \(\bf \cfrac{2}{k}=1\implies \cfrac{2}{1}=k\implies 2=k\) meaning, that, if "k" is 2, then, the EQUATion is true, thus the slopes are equal and thus both lines are parallel, when "k" is 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now... for two lines to be perpendicular their slopes need to be the NEGATIVE RECIPROCAL, that is \(slope=\cfrac{a}{{\color{blue}{ b}}}\qquad negative\implies \cfrac{a}{{\color{blue}{ b}}}\qquad reciprocal\implies  \cfrac{{\color{blue}{ b}}}{a}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and we can negativize and reciprocalize either for that and then find "k"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i do the same thing but just have the slopes as a reciprocal

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf \cfrac{1}{{\color{blue}{ 1}}}\qquad negative\implies \cfrac{1}{{\color{blue}{ 1}}}\qquad reciprocal\implies \cfrac{{\color{blue}{ 1}}}{1}\implies 1 \\ \quad \\ \textit{thus if we equate the 1st one, with THAT negative reciprocal} \\ \quad \\ \cfrac{2}{k}=1\implies \cfrac{2}{1}=k\implies 2=k\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok thnx Cx i get it now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmm actually, should be 2, shoot, missing the negative there \(\bf \cfrac{1}{{\color{blue}{ 1}}}\qquad negative\implies \cfrac{1}{{\color{blue}{ 1}}}\qquad reciprocal\implies \cfrac{{\color{blue}{ 1}}}{1}\implies 1 \\ \quad \\ \textit{thus if we equate the 1st one, with THAT negative reciprocal} \\ \quad \\ \cfrac{2}{k}=1\implies \cfrac{2}{1}=k\implies 2=k\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i just had to do the reciprocal? i thought you had to change the signs too

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because the 2/k was already negative so wouldnt it be k/2 =1 @jdoe0001
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