point on line solver given one component

point_on_line.c

// for the line from [x0,y0] -> [x1,y1]
// given y solve for sx (point on line)
// given x solve for sy (point on line)

const float dx = x1 - x0;
const float dy = y1 - y0;

const float sx = x0 + (y*dx - y0*dx) / dy;
const float sy = y0 + (x*dy - x0*dy) / dx;

// or

const float sx = x0 + (y - y0) * (dx/dy);
const float sy = y0 + (x - x0) * (dy/dx);