A glass cylinder is filled with 50 ml of water. Marbles, each with a volume of 3 ml, are dropped into the cylinder one at a time. With each marble, the water level increases in height by an amount equivalent to a volume of 3 ml. This constant rate of change means there is a linear relationship between the number of marbles and the total volume in the cylinder. If 1 marble is added, the total volume increases by 3 ml. If 2 marbles are added, the total volume increases by 6 ml. If  marbles are added, the total volume goes up ml.

This means that the total volume, , for marbles is . The 3 represents the rate of change, or slope of the graph, and the 50 represents the initial amount, or vertical intercept of the graph.

Any linear relationship can be expressed in the form using just the rate of change, , and the initial amount, . For example, the equation could be used to describe a different scenario where marbles, each with a volume of 5 ml, are added to a cylinder that initially had 20 ml of water.