Question

find the value of k , if 2 X + 3 Y - 1 equal to zero and 4 x + K Y + 2 equal to zero are parallel lines ​

Answer 1

$\textbf{Concept used:}$

$\textbf{If the lines are parallel, their slopes are equal}$

$\text{Given lines are}$

$\textbf{2x+3y-1=0 and 4x+ky+2=0}$

$\textbf{To find: k}$

$\text{Slope of 2x+3y-1=0 is \bf\,m_1=\frac{-2}{3} }$

$\text{Slope of 4x+ky+2=0 is \bf\,m_2=\frac{-4}{k} }$

$\text{Since the lines are parallel, we have}\;m_1=m_2$

$\implies\,\frac{-2}{3}=\frac{-4}{k}$

$\implies\,\frac{1}{3}=\frac{2}{k}$

$\implies\boxed{\bf\,k=6}$

$\therefore\textbf{The value of k is 6}$

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Answer 2

The value of k for the parallel line equation is 6  .

Step-by-step explanation:

Given as :

The line equation are

2 x + 3 y - 1 = 0                      ............1

4 x + k y + 2 = 0                    ..............2

According to question

The two lines are parallel to each other

For standard line equation

i.e  y = m x + c

where m is the slope of the line

For parallel line condition ,Slope of both line are equal

i.e     slope of line 1 = slope of line 2

Now, A/Q

For first line equation

2 x + 3 y - 1 = 0

i.e      3 y = - 2 x - 1

Or,        y = -2/3 x - 1/3

Compare with standard equation

Slope of the line 1 = m =  -2/3

Again

For second line equation

4 x + k y + 2 = 0

i.e      k y = - 4 x - 2

Or,        y = -4/k x - 2/k

Compare with standard equation

Slope of the line 2 = M = - 4/k

Now, From the condition of parallel line equation

i.e         m = M

Or,         -2/3  =  - 4/k

Or,       by cross multiplication

Or,        - 2 × k = 3 × (- 4)

∴            - 2 k = - 12

i.e                k = 6

So, The value of k for the parallel line equation = k = 6

Hence, The value of k for the parallel line equation is 6  . Answer