Question

Find the scalar equation of the line with vector equation (x,y)= (-1,2) + t(3,7), ter.

My friend and I got different answers, I got 0= 7x - 3y + 13, while she got 0= -7x+2y-11

Answer 1

two points on the line (for t=0,1) are (-1,2) and (2,9)
The slope of that line is thus 7/3, so the line will be
7x-3y+k = 0
or
-7x+3y + k = 0
for some k.

Both equations work for (-1,2) but not for (2,9)

Answer 2

picking up from oobleck ...
7x - 3y + k = 0
but (-1,2) lies on it, so
-7 - 6 + k = 0
k = 13

your equation is 7x - 3y + 13 = 0
testing the other point (2,9)
LS = 14 - 27 + 13 = 0 = RS

so both points work