Question

The equation of line L is y=5x+1

Answer 1

Consider the complete question is "The equation of the line $L_1$ is y=5x+1 and the equation of line $L_2$ is 2y-10x+3=0. How can you show that these two lines are parallel?"

Given:

Equation of $L_1$ is $y=5x+1$.

Equation of $L_2$ is $2y-10x+3=0$.

To show:

The these line as parallel.

Solution:

We have,

$y=5x+1$        ...(i)

$2y-10x+3=0$      ...(ii)

Equation (ii) can be written as

$2y=10x-3$

$y=\dfrac{10x-3}{2}$

$y=\dfrac{10x}{2}-\dfrac{3}{2}$

$y=5x-\dfrac{3}{2}$           ...(iii)

Slope intercept form of a line is

$y=mx+b$          ...(iv)

where, m is slope and b is y-intercept.

On comparing (i) with (iv), we get slope of line $L_1$.

$m_1=5$

On comparing (iii) with (iv), we get slope of line $L_2$.

$m_2=5$

Since, $m_1=m_2$, therefore, lines $L_1$ and $L_2$ and parallel because slope of two parallel lines are always equal.

Hence proved.