Question

If the lines represented by 3x+2y+5=0 and kx-6y+4=0 are parallel, then k =

Answer 1

$\textbf{Concept used:}$

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

$\text{Slope of the line ax+by+c=0 is }\;\displaystyle\frac{-a}{b}$

$\text{Now,}$

$\text{Slope of the line 3x+2y-5=0 is, m_1= }\displaystyle\frac{-3}{2}$

$\text{Slope of the line kx-6y+4=0 is, m_2= }\displaystyle\frac{-k}{-6}=\frac{k}{6}$

$\text{Since the lines are parallel,we have}$

$\displaystyle\frac{-3}{2}=\frac{k}{6}$

$\implies\displaystyle\,k=\frac{-18}{2}$

$\implies\boxed{\bf\,k=-9}$

$\therefore\textbf{The value of k is -9}$

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For what value of a the system of linear equations 2x + 3y = 7 and ( a -1 )x + (a + 1)y = 3a + 1 represent parallel lines?​

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