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

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Answer 1 · 2016-06-25T13:24:45

$y=-4x+6$

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

$y=-4x+6$

What is the equation of the line that passes through (1,2)(1,2) and is parallel to the line whose equation is 4x+y-1=04x+y-1=0?