SOLUTION: How do you find the value(s) of k that make two lines parallel? ex. 5x+ky=3 parallel to 6x-4y=6

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Question 771969: How do you find the value(s) of k that make two lines parallel?
ex. 5x+ky=3 parallel to 6x-4y=6
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

5x%2Bky=3 parallel to 6x-4y=6
parallel lines have same slope, find slope first
5x%2Bky=3.....solve for y
ky=-5x%2B3
y=-%285%2Fk%29x%2B3%2Fk.......eq.1..=> slope is -%285%2Fk%29
6x-4y=6
6x-6=4y
y=6x%2F4-6%2F4
y=%283%2F2%29x-3%2F2......eq.2..=> slope is %283%2F2%29
so, -%285%2Fk%29=%283%2F2%29......solve for k
-%285%292=3%2Ak
-10=3k
-10%2F3=k
k=-10%2F3

then 5x%2Bky=3 will be 5x-%2810%2F3%29y=3 or
y=-%285%2Fk%29x%2B3%2Fk will be y=-%285%2F%28-10%2F3%29%29x%2B3%2F%28-10%2F3%29 =>y=%283%2F2%29x-9%2F10
let see them on a graph: