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Let P=(a,b) be the point of intersection of the line y=2x-10 and the line through (7,8) and (-9,0). Compute a+b.

 Jun 15, 2021
 #1
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Find  the  slope of the  second line

 

(  8  - 0 )   / ( 7 - - 9)   =     8  / 16   =   1/2

 

Using  ( -9, 0)   the  equation of this  line  = 

 

y  =  (1/2) ( x  - - 9)

y   =   (1/2)x  + 9/2

 

 

Set  the y's  equal

 

2x -10  =  (1/2) x  +  9/2         multiply  through by 2

 

4x  - 20   =  x  + 9

 

3x  =  29

 

x  =  29/3

 

And y   =  2 ( 29/3)   -10  =   28/3

 

(a , b) = ( 29/3 , 28 /3)

 

(a + b)  =     29/3  + 28/3  =   57 / 3    =    19

 

 

cool cool cool

 Jun 15, 2021

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