A proportional relationship means that one quantity is a constant multiple of another. In the case of the equations you provided:
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For \( y = 3x \), the relationship indicates that for every unit increase in \( x \), \( y \) increases by 3 times that unit increase. This defines a proportional relationship where the constant of proportionality is 3.
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For \( y = 6x \), a similar relationship holds, but here \( y \) increases by 6 times for every unit increase in \( x \), with a constant of proportionality of 6.
Both equations represent proportional relationships, but they have different constants of proportionality (3 and 6, respectively). This means that the values of \( y \) will be different for the same values of \( x \) depending on which equation you are using.
In summary, both equations are proportionally related, but they define different lines in a graph with different slopes.
3 answers