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

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Answer 1 · 2016-06-25T13:24:45

$y = - 4 x + 6$ $y=-4x+6$

Look at the diagram

The given line (Red Colour Line) is -

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

Step - 1

Find the slope of the given line.

It is in the form

$a x + b y + c = 0$ $ax+by+c=0$
Its slope is defined as
$m_{1} = \frac{- a}{b} = \frac{- 4}{1} = - 4$ $m_1=(-a)/b=(-4)/1=-4$

Step -2

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

$m_{2} = m_{1} = - 4$ $m_2=m_1=-4$

Step - 3

The equation of the required line

$y = m x + c$ $y=mx+c$

Where-

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

Find $c$ $c$

$c + m x = y$ $c+mx=y$
$c + (- 4) 1 = 2$ $c+(-4)1=2$
$c - 4 = 2$ $c-4=2$
$c = 2 + 4 = 6$ $c=2+4=6$

After knowing $c$ $c$

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

$y = - 4 x + 6$ $y=-4x+6$
Parallel Lines

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?