what is meant by-non proportional linear relationship?

Loved your response!

I always followed one of the sayings of Albert Einstein, who, loosely stated, said

"Everything should be made as simple as possible, but ...
not too simple."

A non-proportional linear relationship refers to a relationship between two variables where the ratio between them is not constant. In other words, as one variable increases or decreases, the other does not change at a constant rate. This is in contrast to a proportional linear relationship, where the two variables have a constant ratio.

To understand if a relationship between two variables is non-proportional linear, you can use a graph or a table of values.

For example, let's consider the relationship between the number of hours studied for an exam and the corresponding test score. In a non-proportional linear relationship, the test scores may not increase or decrease at a constant rate as the number of hours studied changes.

To determine if the relationship is non-proportional linear, you can plot the hours studied on the x-axis and the test scores on the y-axis. If the graph does not form a straight line or the points do not lie on a straight line, it indicates a non-proportional linear relationship.

Alternatively, you can create a table of values with different numbers of hours studied and corresponding test scores. If the ratios between the test scores and the hours studied are not constant, it indicates a non-proportional linear relationship.

That is an idiotic term invented by math teachers.

Here are examples...

y=3x is a linear equation, proportional.

y=3x-2 is a linear equation, non-proportional.

any linear equation is of the form
y=mx+b

When b is zero, it is a proportional linear equation.
When b is nonzero, it is a "non-proportional" linear equation according to that thinking.

Shakespear wrote Much Ado about nothing, as I recall, but is being reformed here.