In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.

In this example, the constant of proportionality is 3.

Two quantities have a linear relationship when:

• One quantity changes by a set amount, whenever the other quantity changes by a set amount.
• The rate of change is constant.
• The graph of the relationship is a line.

This graph shows a linear relationship between number of days and number of pages read.

When the number of days increases by 2, the number of pages read always increases by 60. The rate of change is constant, 30 pages per day.

The rate of change is the amount \(y\) changes when \(x\) increases by 1. On a graph, the rate of change is the slope of the line.

In this graph, \(y\) increases by 15 dollars when \(x\) increases by 1 hour. The rate of change is 15 dollars per hour.

Graph, horizontal axis, x, amount earned in hours. vertical axis, y, amount earned in dollars. line starting at 0 comma 10, passing through 2 comma 40 and 60 comma 100.

A solution to an equation with 2 variables is a pair of values for the variables that make the equation true.

For example, one solution to the equation \(4x+3y=24\) is \((6,0)\). Substituting 6 for \(x\) and 0 for \(y\) makes this equation true because \(4(6)+3(0)=24\).