Answer
$x=5t-2,y=5t, z=3-5t$
Work Step by Step
The parametric equations of a straight line can be found by knowing the value of a vector, such as $v=v_1i+v_2j+v_3k$, passing through a point $P(x_0,y_0,z_0)$ as follows:
$x=x_0+t v_1,y=y_0+t v_2; z=z_0+t v_3$
Here, we have $P(-2,0,3)$ and $v=\lt 3-(-2), 5-0,-2-3 \gt =\lt 5,5,-5 \gt$
Thus, we get the parametric equations:
$x=5t-2,y=5t, z=3-5t$
