# How do you write the standard form of a line parallel to y-3x=2 and passing through (2,-4)?

Apr 7, 2017

$y - 3 x + 10 = 0$

#### Explanation:

A line parallel to $a x + b y + c = 0$ is of the type $a x + b y + k = 0$

As $y - 3 x = 2$ is $- 3 x + y - 2 = 0$

a line parallel to it will of type $- 3 x + y + k = 0$

Now as it passes through $\left(2 , - 4\right)$, we have

$- 3 \times 2 + \left(- 4\right) + k = 0$

or $k = 6 + 4 = 10$

Hence equation is $- 3 x + y + 10 = 0$ or $y - 3 x + 10 = 0$

graph{(y-3x+10)(y-3x-2)((x-2)^2+(y+4)^2-0.03)=0 [-9.17, 10.83, -6.48, 3.52]}