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yes the independent variable goes on the x-axis
It depends on what you are looking at. If you want to look at changes in variable Y when a variable X is changed, then X is the independent variable and Y is the dependent. But if you want to look at changes in X which accompany changes in Y, then Y is the independent variable and X is the dependent.
Not necessarily. It will be if it is the only independent variable in the system.
the independent variable is on the x-axis
Say y = x2 y is the dependent variable, x is the independent variable.