Not always
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A linear relationship whose graph does not pass through the origin: for example, the relation between temperatures on the Celsius and Fahrenheit scales.
The formula direct variation is xk=y, where k is the constant of variation.Direct variation functions always pass through the origin. Direct variation functions are linear functions (goes in a straight line), except that they pass through the origin. Regular linear functions don't pass through the origin. That is the only difference.
If the question is about a pendulum, the answer is that it should. However, the square-root of the length is directly proportional to the length so that the relationship between the two variables is not linear but quadratic. If the graph is extrapolated accordingly, then it will. There may still be an element of measurement error which may prevent the graph from going exactly through the origin.
It can be either a straight line through the origin or a hyperbola.
It's a slanted straight line that goes through the origin of the coordinates.