Question

For example, Let's say I am graphing a proportional relationship even If it doesn't go through origin and it is an equivalent ratios, Is it proportional or does it have to go throught the origin to be proportional?

Answer 1

A proportional relationship is described by the equation

... y = k·x

The point (x, y) = (0, 0) is always a solution to this equation.

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In short, if the relationship is proportional, its graph will go through the origin. If the graph does not go through the origin, the relationship is not proportional.

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Note that this is true if the domain includes the origin. You can have y = kx for x > 10 and the graph will not go through the origin because the function is not defined there.