Find the value of k if the straight line y = kx + 1 is parallel to the straight line
8x – 2y + 1 = 0.
Answers
Answer:
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Step-by-step explanation:
8x-2y+1=0
8x-2(kx+1)+1=0
8x-2kx-2+1=0
6kx-1=0
6kx=1
k=1/6x.
is answer.
Step-by-step explanation:
Given :-
The lines are y = kx + 1 and 8x -2y + 1 = 0 are parallel to each other .
To find :-
Find the value of k ?
Solution :-
Method-1:-
Given lines are
y = kx + 1
=> kx-y+1 = 0
On comparing with a1x+b1y+c1 = 0 then
a1 = k
b1 = -1
c1 = 1
and 8x -2y + 1 = 0
On comparing with a2x+b2y+c2 = 0 then
a2 = 8
b2 = -2
c2 = 1
Now,
a1/a2 = k/8
b1/b2 = -1/-2 = 1/2
c1/c2 = 1/1 = 1
Given that
The lines are parallel.
We know that
If two lines are parallel then a1/a2 = b1/b2
=> k/8 = 1/2
=> 2k = 8
=> k = 8/2
=> k = 4
Therefore, k = 4
Method -2:-
Given lines are
y = kx + 1 ---------------(1)
and
8x -2y + 1 = 0
=> 2y = 8x+1
=> y = (8x+1)/2
=> y = (8x/2) +(1/2)
=> y = 4x +(1/2) ---------(2)
Given that
The lines are parallel to each other.
We know that
If two lines parallel lines then their slopes are equal.
=> k = 4
Therefore, k = 4
Answer:-
The value of k for the given problem is 4
Used formulae:-
→ If two lines parallel lines then their slopes are equal.
→ If two lines a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are parallel lines then
a1/a2 = b1/b2