Question

Which equation represents the line that passes through the points (1, 1) and (-2, 7)?

Answer 1

`vec u =(-3; 6)`
`vec n=(6; 3)` or `vec n=(-6; -3)`

general equation:
`6x+3y+c=0`

final equation:
`2x+y-3=0`

Explanation:

`A[1; 1]`
`B[-2; 7]`

Now you need to find the directional vector:
`vec u = B - A`
`vec u = (-3; 6)`

With this vector you are able to create the parametric equation, but I gues you want the general equation, so you will need the normal vector.
You create the normal vector form directional by replacing x and y and changing one of signs. There are two solutions:
1. `vec n=(6;3)`
2. `vec n=(-6;-3)`

It does not matter which one of them you will choose.

General equation:
`ax + by + c = 0`
`6x+3y+c=0`

for A (`x=1; y=1`):
`6*1 + 3*1 + c = 0`
`c=-9`

Final equation:
`6x+3y-9=0`
`2x+y-3=0`