If two lines l and m have equations y = -x + 6 and y = -2x + 8, what is the probability that a point randomly selected in the 1st quadrant and below l will fall between l and m? Express your answer as a decimal to the nearest hundredth.
Look at the graph, here : https://www.desmos.com/calculator/40z8d53zzr
The triangle formed by L has a base of 6 and a height of 6...so....its area = (1/2) (6)(6) = 36/2 = 18
The two lines intersect at (2,4)
So.....the area between L and M and below L is a triangle with a base of 2 and a height of 4
And this area = (1/2)(2) (4) = 8/2 = 4
So....the probability of a point being below L and between L and M = 4/18 = 2/9 ≈ 0.22