It is the constant of proportionality.
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If two variables are in direct relationship then the ratio of the two variables is known as the constant of proportion between them. In algebraic form, if X and Y are the two variables, then direct proportionality implies that Y = cX and c is the constant of proportionality.
If you take any pair of variables in the table, their ratio is a constant.
For a direct variation equation the constant MUST be 0. Then the ratio of a pair of values of the two variables is the slope.
It is simply a ratio between two variables. There is no information on what measures the letters represent, nor whether the ratio is a constant or variable (eg between Celsius and Fahrenheit).
The constant of proportionality in the equation y = 3.8x is 3.8. This means that for every unit increase in x, y will increase by 3.8 times that amount. It represents the ratio between the two variables and remains constant throughout the relationship.