Geometry: 78014

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].

Thank you for your answer

Correct 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 4a+3b=60 −2.5b=−90  b=−2.5−90​=36 a=460−3b​=460−3⋅ 36​=−12  a=−12 b=36

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The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
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