Question

a paper mill determined that it can produce 60 cases of paper from 16 treesIs the linear function proportional? How do you know? No, it does not have a constant term added to the variable term. not enough information No, the slope can be written as a decimal. Yes, it does not have a constant term added to the variable term. Yes, the slope can be written as a decimal.

Answer 1

Data:

Number of cases of paper: p= 60

Number of trees: t=16

`p=(60)/(16)t=(30)/(8)t=(15)/(4)t`

Is the linear function proportional? How do you know?

Yes, the linear function is proportional, because the variables (number of cases of paper and number of trees) increase proportionally, It means that the variable number of cases of paper depends of the number of trees, if the number of trees increase, then, proportionally (as always 16 trees makes 60 cases of paper) increase the number of cases of paper.

The slope can be writen as:

`m=(60)/(16)=(15)/(4)=3.75`

A proportional relationship is a function where the line passes throught the origin (0 , 0), as if you have 0 trees you have 0 cases of paper, this is a proportional relationship.

The independient variable is the number of threes, as it doesn't depends of the number of cases of paper.

The dependient variable is the number of cases of paper, it depends of the number of trees.