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Slope  =   [ 1 - - 5]  / [ 6 - -3]  =   6/9  = 2/3

Using  (6, 1)   we have that

y = (2/3) ( x - 6) + 1       multiply through by 3

3y  = 2( x - 6)  + 3

3y  = 2x - 12 +  3

3y = 2x   -  9       rearrange as

2x - 3y  =  9

A = 2     B  =  - 3     C   = 9

A + B + C   =    8