Question

What is the equation of the line that passes through `(1,2)` and is parallel to the line whose equation is `4x+y-1=0`?

Answer 1

`y=-4x+6`

Explanation:

Look at the diagram

The given line (Red Colour Line) is -

`4x+y-1=0`
The required line (Green Colour Line) is passing through the point `(1,2)`

Step - 1

Find the slope of the given line.

It is in the form

`ax+by+c=0`
Its slope is defined as
`m_1=(-a)/b=(-4)/1=-4`

Step -2

The two lines are parallel.
Hence, their slopes are equal
The slope of the required line is

`m_2=m_1=-4`

Step - 3

The equation of the required line

`y=mx+c`

Where-

`m=-4`
`x=1`
`y=2`

Find `c`

`c+mx=y`
`c+(-4)1=2`
`c-4=2`
`c=2+4=6`

After knowing `c`

use the slope `-4` and intercept `6` to find the equation

`y=-4x+6`