# How do you write an equation of a line through (-1,-4) parallel to y=4x+5?

Nov 14, 2016

The equation of the line is $y = 4 x$

#### Explanation:

The equation of a line is $y = m x + c$

where $m$ is the slope.

All parallel lines have the same slope.

$y = 4 x + 5$

The slope is $m = 4$

The equation of a line through $\left({x}_{0} , {y}_{0}\right)$ and of slope $m$ is

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

Here $\left({x}_{0} , {y}_{0}\right) = \left(- 1 , - 4\right)$

Therefore, the equation is $y + 4 = 4 \left(x + 1\right)$

$\implies$ $y + 4 = 4 x + 4$

$\implies$$y = 4 x$
graph{(y-4x)(y-4x-5)=0 [-6.244, 6.243, -3.12, 3.123]}