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 a gradient of -3. The lines L1 and L2 intersect at point P. Find the coordinates of P.

First, we want to find the gradient of L1 using (4,6) and (12,2)m= (2-6)/ (12-4) = -1/2 then we can find the equation of L1 using y=mx+c rearrange for c as the subject, c= y-mx and substitute the gradient and some coordinates: c= 6-(-1/2)(4) = 8 therefore L1: y= (-1/2)x + 8 The equation for L2 is y=-3x
To find P we equate L1 and L2: (-1/2)x+8=-3x
(-5/2)x=8 x= -16/5
y= -3(-16/5) = 48/5