Line integer coefficients

Good day,
Even though it is a trivial task, I don’t know how to deal with it. This is analytic geometry:
Find all integers a, b, and c such that the line given by the equation ax+by=c passes through the points [4,3] and [−2,1]. for your answer

Final Answer:

a =  -12
b =  36
c =  60

Step-by-step explanation:

c=5⋅ 4⋅ 3=60 A=(4,3) B=(−2,1)  A,B∈ p  a⋅ Ax​+b⋅ Ay​=c a⋅ Bx​+b⋅ By​=c a⋅ 4+b⋅ 3=60 a⋅ (−2)+b⋅ 1=60  4a+3b=60 2a−b=−60  Row2−42​⋅ Row1→Row2 −2.5b=−90  b=−2.5−90​=36 a=460−3b​=460−3⋅ 36​=−12  a=−12 b=36

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