Question

Are linear relationships sometimes, always, or never examples of directly proportional relationships

Answer 1

Sometimes

Example:
As the number of DVDs you buy increases the total cost is added by 12$

For example,
1 DVD - 12$
2 DVD - 24$
3 DVD - 36$
...
100 DVD - 1200$

Hence, the relationship is proportionate.
It introduces the relationship between two variables and is called correlation. Proportionality or variation is state of relationship or correlation between two variables It has two types: direct variation or proportion which states both variables are positively correlation. It is when both the variables increase or decrease together. On the contrary, indirect variation or proportion indicates negative relationship or correlation. Elaborately, the opposite of what happens to direct variation. One increases with the other variables, you got it, decreases. This correlations are important to consider because you can determine and identify how two variables relates with one another. Notice x = y (direct), y=1/x (indirect)