I currently started with some basic geometry and I'm already stuck at some very very basic intuition regarding finding the line between two points in a plane.
I understand $y = mx + c$ and I am able to calculate all variables. The way I calculated $c$ thus far has been by finding the slope, and use one point in the plane to find the remainder as $c$ through $y = mx + c$.
Now the textbook used the following points: $A: (-1, -1)$ and $B: (1, 2)$ which results in $y = \frac{3}{2}x+\frac{1}{2}$ and I was able to do this myself by hand.
However, a different method without using one point and a calculcated slope involves using the following equation:
$$ c = \frac{x_2y_1 - x_1y_2}{x_2-x_1} $$
But I cannot wrap my head around or find the intuition as to why I am multiplying $x_2$ with $y_1$ and subtracting $x_1$ multiplied by $y_2$.
Considering we're dividing by $x_2 - x_1$ it must have something to do with the differences in $y$. I've calculcated both products but I don't see some sort of relation.
As a test case I used a formula I just came up with: $y = 3x + 4$ and took points $C: (-2, -2)$ and $D: (4,16)$ just to have another example but I am still stuck with why I am doing this and what the products: $x_2*y_1=4*-2=-8$ and $x_1*y_2=-2*16=-32$ tell me.
$\frac{24}{6}$ obviously is $4$ which would be the correct $c$. Yet I am missing intuition and I really want to understand this. Can someone help me?