# Thread: Equation of the line that goes through the point and is parallel

1. ## Equation of the line that goes through the point and is parallel

I just started this an the book does not explain it well. can you give me the basics for solving something like this:

Find the equation of the line that goes through the point (-1,2) and is parallel to the line -x - 3y +1 = 0

Honestly I have no idea how to proceed =\

2. Originally Posted by mrnemo
I just started this an the book does not explain it well. can you give me the basics for solving something like this:

Find the equation of the line that goes through the point (-1,2) and is parallel to the line -x - 3y +1 = 0

Honestly I have no idea how to proceed =\
1. If the 2 lines are parallel then they have equal slopes:

$-x+3y+1=0~\implies~y = \frac13 x-\frac13$

That means the new line must have the slope $m = \frac13$

2. The equation

$y-y_1 = m(x-x_1)$

describes a line passing through the point $P(x_1, y_1)$ with the slope m.

3. I'll leave the rest for you.

3. Thank you. I think I got it.