How do you find the equation of a line in standard form (ax+by=c where a, b, and c are integers) for the line passing through (1,5) and (-3,1)?

Answer 1

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Two-point form of equation:

y - y1 = [ ( y2 - y1 ) * ( x - x1 ) ] / ( x2 - x1 )

In this case:

x1 = 1

x2 = -3

y1 = 5

y2 = 1

y - 5 = [( 1 - 5 ) * ( x - 1 )] / [ ( -3 ) - 1 ) ]

y - 5 = ( -4 ) * ( x - 1 )/ ( -4 )

y -5 = ( - 4 / -4 ) * ( x - 1 )

y - 5 = 1 * ( x - 1 )

y - 5 = x - 1

y - x = -1 + 5

y - x = 4

Ax + By = C

A = 1

B = -1

C = 4