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Well, isn't that a happy little question! A non-example of a constant of proportionality would be a relationship where the ratio between two quantities is not always the same. Imagine a situation where the more you paint, the less paint you use each time - that would not have a constant of proportionality. Just like in painting, it's all about finding balance and harmony in the relationships around us.
A straight line, through the origin, sloping up from left to right. The gradient of the graph will be the constant of proportionality.
A line graph.
Constant variation is a relationship between two variables where one is a fixed multiple of the other. The graph of such a relationship is a straight line through the origin.
A graph shows a proportional relationship if it is a straight line that passes through the origin (0,0). This indicates that as one variable increases, the other variable increases at a constant rate. Additionally, the ratio of the two variables remains constant throughout the graph. If the line is not straight or does not pass through the origin, the relationship is not proportional.