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What is the area, in square units, of the interior region formed by the lines y = 2x - 4, y = -3x +16 and the y-axis?

waffles  Nov 21, 2017
edited by waffles  Nov 21, 2017
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 #1
avatar+79894 
+1

I'm assuming that you mean the x axis

 

We have a triangular area...

 

The line y  = 2x - 4    and y =  -3x + 16  intersect at the x value

 

2x - 4   =  -3x + 16

5x  =  20

x =4

So...x =  2(4) - 4  =  4

 

And the y coordinate is  2(4) - 4  = 4....and thid the height of the triangular aresw

 

And   y = 2x - 4   intersects the x axis at x =  2  

And y = -3x + 16   intersects the x axis at  16/3

 

So....we have a triangle with a base of  [ 16/3 - 2]   = 10/3    and a height of 4

 

So....the area is     (1/2)(10/3) (4)   =  20/3 units^2

 

 

cool cool cool

CPhill  Nov 21, 2017
 #2
avatar+428 
0

i made a edit

waffles  Nov 21, 2017
 #3
avatar+79894 
+1

OK....

 

We have a  triangle with a height of 4 and a base of 20

 

So....the area is  (1/2)(20)(4)  =  40 units^2

 

Here's the graph : https://www.desmos.com/calculator/ktl6nn6onh

 

cool cool cool

CPhill  Nov 21, 2017

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