G: the weight of a bag of pennies, given the number of pennies
Work Step by Step
This is the only relation that can be matched with a linear function because each penny has a constant weight and as you add each penny in the bag, the weight of the bag will change by a constant amount. Whereas, in the other examples, the given variables like height, length of a day, and test grade do not increase or decrease by a set amount. Lets look at example F. A person does not increase its height by a constant amount each day. Many factors come into play like nutrition, exercise and etc. For example H, the length of a day does not change by a constant amount as days progress. Also in example I, your test grade does not change by a constant amount as you increase your studying time. It is not like if you study 1.5 minutes more, you will get a higher test grade. Many factors play a role in deciding each scenarios ranges so therefore we cannot represent them with a linear function.