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The y-axis is the vertical axis on a graph.
The origin is where x axis and y axis intersect.
The y axis is going up on the graph and the x axis is going sideways on the graph
Typically the y-axis is the vertical axis and x-axis if horizontal. This is by convention and not required.This is used to plot a binomial (two variable) equation.
The horizontal axis of a typical graph would be the "X-axis"