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point B will be any point on the perpendicular bisector of AC.
as such it will be equidistant between A and C which will always make AB = BC.
the linear relationship is the equation of the line that passes through the midpoint of AC and is perpendicular to it.
the equation of the line AC is:
y = (3/5)x + (13/5)
the equation of the line perpendicular to AC and passing through its midpoint is:
y = -(5/3)x + 6
the graph of the equations for those line is shown below:
point B is any point on the line perpendicular to AC, so the linear relationship between the x value of that point and the y value of that point is the equation of the line perpendicular to AC which is the equation:
y = -(5/3)x + 6.
a picture of the relationship is shown below:
line DE is perpendiculat to line AC.
any point on line DE is equidistant from A and C.