Final answer:
To find the parametric equation of a line that is parallel to a given line and passes through a given point, use the direction vector of the given line and the given point to create the parametric equations.
Step-by-step explanation:
To find the parametric equation of a line parallel to the given line, we need to use the direction vector of the given line and the given point to find the parametric equations.
The given line can be represented as:
x = 12t
y = -t
z = 2
Since the direction vector of this line is (12, -1, 0), any line parallel to this line will have the same direction vector.
Therefore, the parametric equations for the line passing through the point (2, 0, -1) and parallel to the given line are:
x = 2 + 12t
y = 0 - t = -t
z = -1 + 0t = -1