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What does a direct proportion look like on a graph?
A straight line, through the origin, sloping up from left to right. The gradient of the graph will be the constant of proportionality.
Does a constant of proportionality exist?
Yes, it does. Every time there are variables in direct or inverse relationship, there is a constant of proportionality.
If y equals kx then what is the relationship between x y and k?
Various options: y is directly proportional to k, with x as the constant of proportionality; y is directly proportional to x, with k as the constant of proportionality; x is inversely proportional to k, with y as the constant of proportionality; x is directly proportional to y, with 1/k as the constant of proportionality; k is directly proportional to y, with 1/x as the constant of proportionality; and k is inversely proportional to x, with y as the constant of proportionality.
What is a constant ratio of two variables that are related proportionally?
It is the constant of proportionality.
What is a non example of a constant of proportionality?
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.
