Question

Check whether the pair of lines $7x+y+3=0$ and $14x+2y+5=0$ is parallel or not.

Answer 1

Step 1:Finding the slope of $7x+y+3=0$:

The given equation $7x+y+3=0$ can be written as :

$y=-7x-3$

On comparing with the general equation of a line $y=mx+c$

The slope of line $\left(m_1\right)=-7$……………………….(1)

Step 2:Finding the slope of $14x+2y+5=0$:

$$\begin{gathered} 14x+2y+5=0 \\ \Rightarrow 2y=-14x-5 \\ \Rightarrow y=-7x-\frac{5}{2} \end{gathered}$$

On comparing with the general equation of a line $y=mx+c$

The slope of line $\left(m_2\right)=-7$……………………………(2)

Step 3:Verifying that both the lines are parallel:

Two lines are said to be parallel if their slopes are equal

On comparing equations (1) and (2)

$m_1=m_2=-7$

Hence ,both the given lines $7x+y+3=0$ and $14x+2y+5=0$ are parallel.