Parametric equation of line parallel to given line through point P(5,1,6)

[tarheels88]

Homework Statement

A line L passes through the point P(5,1,6) and is parallel to the line M with given parametric equations x=4+4t, y=8+5t, z= 9t. Find the parametric equation of the line L.

Homework Equations

Well the things that I do know is that the vector to this problem is <4, 5, 9> and the points on the parametric equation given is (4, 8, 0).

The Attempt at a Solution

I had the two points up to get (-1, 7, -6) so the line L would equal..
x=-1+4t, y=7+5t, z=-6+9t

Is this correct?

 

[ehild]

Does your line pass through the point P(5,1,6)? At what value of the parameter t?

The direction vectors of parallel lines are the same, so you found out correctly that it is (4,5,9) for the new line.

The line goes through a point which corresponds to t=0. If the equations defining the line are x=a+4t, y=b+5t, z=c+9t, then the line passes through the point (a,b,c). But you know that it passes through the point P(5,1,6), so what can be a, b, c?