Answer
$x=4t,y=3t,z=-t$
and
$\frac{x}{4}=\frac{y}{3}=\frac{z}{-1}$
Work Step by Step
The direction vector for a line through the origin $(0,0,0)$ and the point $(4,3,-1)$ is $\lt 4,3,-1 \gt$ .
Parametric equations defined by:
$x=x_0+at$, $y=y_0=bt$ and $z=z_0+ct$
Thus, the parametric equations are:
$x=4t,y=3t,z=-t$
The symmetric equations are defined by:
$\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}$
Hence, the symmetric equations are:
$\frac{x}{4}=\frac{y}{3}=\frac{z}{-1}$
