There are basically SEVERAL continuity equations, one for each conserved quantity. The equations themselves are simply statements that matter (in the example of conservation of mass) will not appear out of nothing, or suddenly teleport to a far-away place.
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derivation of pedal equation
http://en.wikipedia.org/wiki/Navier-Stokes_equations Please go to this page.
They could be the coordinates of a straight line equation
Yes if it is a straight line equation
You can either measure or estimate the coordinates visually from the graph, or solve the equation underlying the graph.