Question

Match the given pairs of lines with the relation between them.

• A. Co-incident
• B. Perpendicular
• C. Parallel

Answer 1

Case 1:
The pair of line given by the equations $2x+4y=4,6x+12y=12$ are co-incident as if you multiply the equation of the first line by 3, you will get the equation of second line.
$3\times (2x+4y)=3\times 4$

Case 2:
The pair of line given by the equations $x+2y=3,2x-y=12$ ,
slope of the line $x+2y=3=\frac{-1}{2}$ $=m_1$
slope of the line $2x-y=12=\frac{2}{1}$$=m_2$
Since, the product of the slopes $m_1\times m_2=-1$ , the lines are perpendicular with respect to each other.

Case 3:
The pair of line given by the equations $2x+4y=4,4x+8y=12$
slope of the line $2x+4y=4$
= $\frac{-2}{4}$ $=-\frac{1}{2}$$=m_1$
slope of the line $4x+8y=12$
= $\frac{-4}{8}$ = -$\frac{1}{2}$$=m_2$
$\Rightarrow m_1=m_2$
Since, the slopes of the lines are equal, the lines are parallel with respect to each other.