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Find a if the point (3,a) is on the line that passes through (-2,7) and (5,-8).

 May 28, 2021
 #1
avatar+119895 
+2

The  slope  of  the line  is

 

[ -8 - 7 ]  /   [ 5 - -2 ]    =   -15 / 7

 

Since   ( 3, a)  is  on  the line....we  can solve fro "a"   thusly

 

[ 7 - a ]  /  [ -2 - 3 ]     =    -15/7

 

[ 7 - a ]  /  - 5   =  -15/7              multiply through  by   -5

 

7 - a   =  75/7         rearrange  as

 

7  - 757  =  a

 

(49/7) - (75/7)  =  a

 

-26/7   =  a

 

 

cool cool cool

 May 28, 2021
 #2
avatar+32678 
+2

it is

from -2 to 5   is a distance of 7     we want 5/7 of this to get to 3   (from 2)

   for a   from 7 to -8 is a 'distance' of -15         5/7 * (-15) added to 7 = -75/7  + 7 =  - 26/7      ( as Chris found ....!)

 May 28, 2021

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