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What is the intersection point of the line $y = 2x + 5$ and the line perpendicular to it that passes through the point $(5, 5)$?

 Jul 13, 2019
 #1
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y =  2x + 5

 

In the form   y =  mx + b.....the slope  = m = 2

 

And the slope of a perpendicular line  = -1 /m =  -1 /2

 

So...the equation of the perp line passing through  (5,5)  is

 

y  = (-1/2) (x - 5) + 5

 

y  = (-1/2)x + 5/2 + 10/2

 

y  = (-1/2)x  +  15/2

 

So....to find the intersection point.....set the y's equal

 

2x + 5   =   (-1/2)x + 15/2       

 

(5/2)x  =  15/2 - 10/2

 

(5/2)x  = 5/2   ⇒    x  = 1

 

And y  = 2(1) + 5  =  7

 

So...the intersection point is  (1,7)

 

Here's a  graph : https://www.desmos.com/calculator/qk27oulorw

 

 

cool cool cool

 Jul 13, 2019

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