Line L1 passes through points (4,6) and (12,2). Line L2 passes through the origin and has gradient -3. The two lines intersect at point P. Find the co-ordinates of P.

Gradient of L1 : Gradient = Change in y/ Change in x. Gradient = (2-6)/(12-4)= -1/2
Gradient is "m" in y=mx+cPlug in a point to determine c : 6 = -1/2 *4 + c --> c =8 L1 is given by y=-1/2x +8
L2 has gradient m of -3, and passes through origin so is given by y=-3x
Set L1 and L2 equal: -3x=-1/2x+8 , so -5x =16, x=-16/5, y = 48/5