Represent linear relations using tables

Detailed Explanation: Represent linear relations using tables

A table represents a linear relation by matching each input with its corresponding output.

• The independent quantity is the input. You choose its value.
• The dependent quantity is the output. Its value depends on the input.
• In a linear relation, equal increases in the input produce equal increases in the output.

Example: A gym charges a one-time fee of $5 plus $3 for each class attended. Make a table showing the total cost for different numbers of classes.

Let

• $x$ = number of classes, the independent quantity
• $y$ = total cost in dollars, the dependent quantity

The cost rule is

The $5$ is the initial fee, and $3$ is the cost for each class.

Choose input values for $x$ and calculate the matching output:

So the table is

Each row gives an ordered pair:

Notice that when the number of classes increases by $1$, the cost always increases by 3$:

This constant change shows that the table represents a linear relation. The value $5$ is the initial value because it is the output when $x=0$.