The straight line L1 passes through the points with coordinates (4, 6) and (12, 2) The straight line L2 passes through the origin and has gradient -3. The lines L1 and L2 intersect at point P. Find the coordinates of P.

First, find equations for the 2 lines in the standard cartesian form y=mx+c:L1: To find gradient = dy/dx = change in y/change in x = (y2-y1)/(x2-x1) = (2-6)/(12-4) = -4/8 = -0.5 = m To find intercept use gradient and one of the points: 6 = -0.54 + c -> c=6+2=8 y=-0.5x+8L2: y=-3xEquate the 2 lines to find the x-coordinate of P: -3x=-0.5x+8 -> -2.5x = 8 -> x = -8/2.5 = -3.2 -> y=-3-3.2 = 9.6P has coordinates (-3.2,9.6)