Question

Which table shows a proportional relationship between the number of books purchased and the cost of the books?And don't worry this is just a practice :)

Answer 1

By definition, an equation of a Proportional relationship has the following form:

`y=kx`

Where "k" is the Constant of proportionality.

In this kind of relationship, the when the value of "x" increases, the value of "y" increases (and the ratio between them does not change); and when the value of "x" decreases, the value of "y" also decreases (and the ratio between them does not change.

Knowing that, you can analize each table:

Table A:

You can see that when the "Number of books" increases, the "Cost" increases. But you need to check if the ratio between them changes:

`(Cost)/(NumberOfBooks)`

Then:

`(8)/(1)\\e(24)/(4)`

It is not a Proportional relationship.

Table B:

You can see that when the "Number of books" increases, the "Cost" increases. But you need to check if the ratio between them changes:

`(8)/(1)=(32)/(4)\\e(54)/(9)`

It is not a Proportional relationship.

Table C:

When the "Number of books" increases, the "Cost" increases, but you need to check if the ratio between them changes:

`(10)/(2)\\e(15)/(4)`

It is not a Proportional relationship.

Table D:

When the "Number of books" increases, the "Cost" increases. Check if the ratio between them changes:

`(16)/(2)=(40)/(5)=(48)/(6)=(120)/(15)=8`

Table D shows a proportional relationship between the number of books purchased and the cost of the books.