# How do you write an equation of a line through (4,-1) and parallel to y= 2x +1?

Sep 7, 2016

Equation of line parallel to $y = 2 x + 1$ and passing through $\left(4 , - 1\right)$ is $y = 2 x - 9$

#### Explanation:

Equation of a line parallel to $y = 2 x + 1$ is

$y = 2 x + k$

As it passes through $\left(4 , - 1\right)$, we have

-1=2×4+k or

$- 1 = + 8 + k$ or

$k = - 8 - 1 = - 9$

Hence, equation of line parallel to $y = 2 x + 1$ and passing through $\left(4 , - 1\right)$ is $y = 2 x - 9$