Question

I need to find a set of a parametric equations for these lines. (see picture) thanks!?!

Answer 1

First option where `x=-3+9t` and `y=2+3t`

Explanation:

The slope of line passing through `(-3,2)` and `(6,5)`

is `(5-2)/(6-(-3))=3/9=1/3`

Hence for every increase of `1` unit in `y`, there should be `3` unit increase in `x`.

This is seen only in first and second options, as when `t` rises by `1`, `x` rises by `9` and `y` rises by `3`.

When `t=0`, while first option gives `x=-3` and `y=2`, Similarly for `t=1`, `x=6` and `y=5` i.e. line passes through `(-3,2)` and `(6,5)`

in second option `x=-3`, when `t=-6/9=-2/3` and then `y=-4`. Similarly in this option, when `x=6`, `t=1/3` and `y=-1`. Hence line passes through `(-3,-4)` and `(6,-1)`

i.e. answer is first option where `x=-3+9t` and `y=2+3t`