If the line passes the origin then to find equation you need to check coordinates of points:
[tex]P_1=(3,\,5)\quad\implies\quad y=\dfrac53\,x\\\\P_2=(3,\,3)\quad\implies\quad y=\dfrac33\,x\quad\implies\quad y=x\\\\P_3=(3,\,1)\quad\implies\quad y=\dfrac13\,x\\\\P_4=(3,\,-2)\quad\implies\quad y=\dfrac{-2}3\,x\quad\implies\quad y=-\dfrac23x\\\\P_5=(3,\,-4)\quad\implies\quad y=\dfrac{-4}3\,x\quad\implies\quad y=-\dfrac43x\\\\P_6=(3,\,-6)\quad\implies\quad y=\dfrac{-6}3\,x\quad\implies\quad y=-2x[/tex]
