What is Proportionality?

Example 44.2

Notebooks at $2$ euros each:

Each price is the number of notebooks $\times 2$: the coefficient is $2$ (the unit price). A quick check that a table is proportional: all the “column quotients” $\frac{6}{3}, \frac{10}{5}, \frac{16}{8}, \frac{24}{12}$ must be equal — here they all equal $2$.

Example 44.3 (A non-example)

Age and height are not proportional: a $12$-year-old is not twice as tall as a $6$-year-old. Check on numbers: $1.50$ m at $12$ years and $1.15$ m at $6$ years give quotients $\frac{1.50}{12} = 0.125$ and $\frac{1.15}{6} \approx 0.19$ — not equal.