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If two lines l and m have equations y = -x + 8, and y = -4x + 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.

 Jan 9, 2021
 #1
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The line  y = -x + 8  will form a triangle in the  first quadrant with  a height of 8  and a base of 8

 

The line  y =  -4x +  8   will form a triangle in the  first quadrant with a height of 8  and a base of 2

 

So  a triangle formed   in the 1st quadrant  by  the intersection of these two lines  will have a base of  6

 

So....the probability  that  a point  selected  in the  first quadrant and below   l   will fall between l and  m  =

 

6/8   =  3/4  =   .75      

 

See the graph here  : https://www.desmos.com/calculator/qwfb7aqtth

 

cool cool cool

 Jan 9, 2021

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