Equation of line passing through 2 points

#include<bits/stdc++.h>
#define ll long long

// input: 2 points
// output: (a, b, c) represents the equation: ax + by = c   
template <typename T> vector<T> line_passing_2_points(T x1, T y1, T x2, T y2) {
    T a = y2 - y1; 
    T b = x1 - x2; 
    T c = a*(x1) + b*(y1); 
    
    
    T gcd;
    gcd = __gcd(a, b);
    gcd = __gcd(gcd, c);
    
    a/= gcd;
    b/= gcd;
    c/= gcd;
    
    
    if (a < 0) {
        a = -a;
        b = -b;
        c = -c;
    }
    
    vector<T> line = {a, b, c};
    return line;
}