If two lines $l$ and $m$ have equations $y = -x + 6$, and $y = -4x + 6$, 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.

Lightning
Mar 29, 2018

#1**+2 **

The area below l and still in the first quadrant is a triangle with a base of 6 and a height of 6

So...its area is base * height /2 = 6 * 6 /2 = 18 units^2 (1)

The area between the two lines also forms a triangle with a height of 6 and a base of 4.5

So...its area is 6 * 4.5 / 2 = 13.5 units^2 (2)

So...the probability of a point being selected in the specified area is (2) / (1) =

13.5 / 18 = 0.75

CPhill
Mar 29, 2018