Given 2 points eg. $(x_1, y_1), (x_2, y_2)$ how do I express in $ax + by + c$ form?
I am supposed to find the intersection of 2 lines. I have 2 points for 1 line, and the other line will be something like $y=10$. I think my maths is very rusty and don't really get it ...
I guess $t$ is a variable, $x_i, y_i$ values are given, but whats $a, b, c$?
Think of the segment as a line that passes through $p_0$ and $p_1$. Find the slope of that line. You can denote it as $m$ and find using the following formula:
$$m = \frac{y_0-y_1}{x_0-x_1}$$
Then you can find the equation of that line using the same formula:
$$y - y_0 = m(x - x_1)$$
And you'll get an equation for the line of the tupe $Ax + By + C = 0$
Once you find them solve the following system of equations:
$$ \left\{\begin{aligned} &Ax + By + C = 0\\ &ax + by + c = 0 \end{aligned} \right.$$
A,B,C and a,b,c are coefficient in the equation of the line that define that line.