Find symmetric equations for the line. (Use the parameter t.)

Question

The line through
(−8, 4, 7)
and parallel to the line
x/2= y/3= z+1

Answer 1

well, the given line goes through (0,0,-1) right?

Answer 2

The new line must have the same direction as x/2 = y/3 = z+1, which means that the new line must have direction (2,3,1) and must pass through the point (−8, 4, 7).

parametric equations of new line:
x = -8 + 2t
y = 4 + 3t
z = 7 + 1

The fact that (0,0,-1) in on the given line, has no impact on the new line

Answer 3

no, it does not. But the given symmetric equations can be used as a model for the desired equations. (not parametric, btw)

which can also be derived from yours, by eliminating t.

Answer 4

missed the "symmetric" part and assumed parametric, by bad

so we could just go ...

(x+8)/2 = (y-4)/3 = z -7