# How do I find an equation of the line that passes through the points (2, -1, 3) and (1, 4, -3)?

Oct 19, 2014

Let

$\left({x}_{0} , {y}_{0} , {z}_{0}\right) = \left(2 , - 1 , 3\right)$,

and let the direction vector

$\left(a , b , c\right) = \left(1 , 4 , - 3\right) - \left(2 , - 1 , 3\right) = \left(- 1 , 5 , - 6\right)$.

Since the parametric equations of the line can be written as

$\frac{x - {x}_{0}}{a} = \frac{y - {y}_{0}}{b} = \frac{x - {z}_{0}}{c}$,

we have

$\frac{x - 2}{- 1} = \frac{y + 1}{5} = \frac{x - 3}{- 6}$.

I hope that this was helpful.