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A line passes through the points (-3,-5) and (6,7). The equation of this line can be expressed in the form Ax + By = C, where A, B, and C are integers with greatest common divisor 1, and A is positive. Find A + B+ C.

 Aug 5, 2022
 #1
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Slope  =    ( 7 - -5) / ( 6 - -3)  =  12/9  = 4/3

 

Using either point  we can write the equation  as

 

y = (4/3) (x - 6) + 7          multiply through by 3

 

3y  = 4(x - 6) + 21

 

3y =  4x - 24 + 21

 

3y  = 4x  - 3             rearrange as

 

4x - 3y  =  3

 

A  +  B + C  =   4   -3  + 3   =    4

 

 

cool cool cool

 Aug 5, 2022

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