In the next lesson, you will need to use information about a relationship to complete a table and graph points on a coordinate plane. Refer back to a problem you examined in the topic Multi step problems, when you investigated whether it would cost more for Jenna to drive her own car or a rental car. As part of that lesson, you looked at the relationship between the cost of gas and the cost (in $/mile) for Jenna to drive her car. You have also learned in previous lessons how algebra can be used to express relationships between variables. Now you are going to expand this idea as you study four representations of a mathematical relationship.
Model or equation
In Multi step problems, your class wrote a mathematical equation for the relationship between the cost of gas and the cost of driving. An equation is useful because it can be used to calculate the cost values. As you saw with the formula for braking distance in the topic Algebraic formulas, equations are also useful for communicating complex relationships. In writing equations, it is always important to define what the variables represent, including units. For example, in the equation that represents the relationship between the cost of gas and the cost of driving, the variables were defined as shown below. Note that each definition includes what the variable represents, such as the cost of Jenna’s car, and the units in which this quantity is measured, such as $/mile.
Cost of Jenna’s car in $/mile
Price of gas ($/gal)
These variables were used in the mathematical equation,
.
Table
Another way that you could have represented this relationship between the price of gas and the cost of driving the car is in a table that shows values of g and J as ordered pairs. An ordered pair consists of two values that are matched together in a given relationship. You used this representation in Multi step equations when you explored how changes in one variable affected another variable. Tables are helpful for recognizing patterns and general relationships or for giving information about specific values. A table should always have labels for each column. The labels should include units when appropriate.
Price of gas
($/gal) Cost of driving Jenna’s car
($/mile)
3.00 0.28
3.50 0.31
4.00 0.33
4.50 0.35
Graph
In the last few assignments, you practiced graphing. A graph provides a visual representation of a situation. It helps you see how the variables are related to each other and to make predictions about future values or values in between those in your table. The horizontal and vertical axis of the graph should be labeled, including units.
Jenna Driving Cost graph]