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What is the area, in square units, of the interior region formed by the lines $y = 4x - 6, y = -2x +12$ and the $y$-axis?

 Jun 24, 2018
 #1
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+1

18/2=9*3=27

 Jun 25, 2018
 #2
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+2

 

This region will form a triangle

 

To find the height of this triangle, let us fihd the x value of the intersection of the lines....set the y's  equal

 

4x  - 6  = -2x + 12     add 2x to both sides, add 6 to both sides

 

6x  = 18     divide both  sides by  6

 

x  = 3         this x value will be the height of the triangle

 

And the y intercept of 4x  - 6  =   -6

And the y intercept  of  -2x + 12  = 12

 

So....the length of the base of this triangle  =  12 - (-6)   = 18

 

So....the area of the tiriangle is  (1/2) (base length) (height)  =  (1/2)(18)(3)   = 27  units^2

 

Here's a pic :

 

https://www.desmos.com/calculator/9svh83h2ij

 

cool cool cool

 Jun 25, 2018

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