State a direction vector for each of the following lines. A line parallel to x=9-3t, y=-4+t

Answer 1

Since x=9-3t, this means that x-9=-3t, which implies t=-(x-9)/3.

Similarly, since y=-4+t, this means that t=y+4.

Therefore, we can express the line as:

x-9=-3(y+4)

Simplifying this equation, we get:

x+3y+3=0

This is the equation of the line in the standard form Ax+By+C=0, where A=1, B=3, and C=3.

So a direction vector for this line is <1, 3>.