Equation of line passing through two points [tex](x_{1},y_{1}), and (x_{2},y_{2}) is[/tex]=[tex]\frac {y-y_{1}}{x-x_{1}}=\frac{y_{2} - y_{1}}{ x_{2}-x_{1}}[/tex]
Now , we will find first equation of line which passes through (-4,4) and (-2,0) is :
[tex]\frac{y-4}{x+4}= \frac{0-4}{-2+4}\\\\\frac{y-4}{x+4}= \frac{-4}{2}\\\\y-4 = -2 x -8\\\\y +2 x +4=0[/tex]
The Second line which passes through (0,-4) and (2,-8) is :
[tex]\frac{y+4}{x-0}= \frac{-8+4}{2-0}\\\\\frac{y+4}{x}= \frac{-4}{2}\\\\y+4 = -2 x \\\\y +2 x +4=0[/tex]
So equation of line passing through (-4,4) , (-2,0) ,(0,-4) and (2,-8) is :(All points are collinear, so there will be unique line passing through these four points.)
2 x + y + 4=0
