Verify if correct.

Question

Determine which line is parallel to the line with Cartesian equation 2x +3y + 5=0

a) r=(-1,-1) +s(2,3), seR

b) x=3t-1, y=-2t-1, teR

c) x=2t-1, 3t-1, teR

d) none of the above.

I chose D, none of the above because none of them are multiples of the given equation 2x+3y+5=0.

Thank you!

Answer 1

look at b) , and sub into the line equation

LS = 2x + 3y + 5
= 2(3t-1) + 3(-2t-1) + 5
= 6t-2 -6t-3 + 5
= 0
= RS

not only are they parallel, but they represent the same line