# How do you write an equation of a line through (6, 2); parallel to 4x-y=3?

Dec 5, 2016

I got: $4 x - y = 22$

#### Explanation:

We can use the general expression for a line through a point of coordinates $\left({x}_{0} , {y}_{0}\right)$ and slope $m$ as:

$y - {y}_{0} = m \left(x - {x}_{0}\right)$

The slope must be the same of the slope of the original line in order to be parallel.

The original line can be written (collecting $y$) as:
$y = 4 x - 3$
where the slope will be: $m = 4$ (the coefficient of $x$):
so we have:
$y - 2 = 4 \left(x - 6\right)$
$y = 4 x - 24 + 2$
$y = 4 x - 22$
or
$4 x - y = 22$