Note the distance from [1,2] to [13,7] is sqrt(12^2 + 5^2) = 13, so at t = 2 seconds, P = [13,7]. So the speed in the x-direction is 12/2 = 6 ft/sec and the speed in the y-direction is 5/2 ft/sec. So the equations are x = 1 + 6*t, y = 2 + 5/2*t.