I had to parameterize a straight line with starting point in $A=(-3,7)\\ $ and endpoint in $B=(4,1)$.
My idea was to use the equation for the line that goes through two points. That is:
$ \frac { y\quad -\quad { y }^{ 1 } }{ x\quad -\quad { x }^{ 1 } } =\frac { { y }^{ 2 }\quad -\quad { y }^{ 1 } }{ { x }^{ 2 }\quad -\quad { x }^{ 1 } } $
When solving it, I had:
$ y\quad =\quad -\left( \frac { 8x\quad -\quad 25 }{ 7 } \right) $
Which after I plotted, ended up with a straight line passing by the given points of the exercice. I was happy, until my teacher advised me of a "very easy way" to do this, which I should "already know", and it's to find out the position of the line using polar coordinates.
I have been reading about the subject, but as far as I understand, I need two things: the length from $A$ to $B$ and then the angle of said line against the X axis, am I right? I find this a bit confusing. I would like to know if my equation is really a bad way to do this, and in case that polar coordinates are the best way to parameterize this exercise, I don't understand which operation should I do to find out the angle, assuming I already know the starting and endpoint of AB.
Thank you for any help! I have been one whole day thinking about this and I am sure I am missing something very obvious.