Graphing with Variation

The relationships between the changing quantities can be examined by using a model of data that illustrates how the change in one variable affects a second variable.

A graph can also illustrate a direct variation. The graph below shows the line changing at the same rate. We know this because it is a straight line. If the line was not straight, we would not have a direct variation.

To graph a direct variation, there are several steps that need to be followed. Before we can follow the steps, we first need to discuss graphing in general. Here we need to rely on our knowledge of graphing to plot points that we connect to create a graphed line.

Graphing

Making Sense of Graphs

The graph below shows the amount of money required to buy gasoline if the cost per gallon is $2.00.

1. What two quantities vary proportionally in this situation?

ANSWER: The number of gallons and the price of gas

2. What is the value of the constant of proportionality? What does this value represent in the context of the problem? How is the constant of proportionality represented on the graph?

text annotation indicator ANSWER: The constant of proportionality is 2 which is the cost per gallon of gas. It is k in the equation y=kx where y=2x. It is also the slope of the line on the graph (rise/run)

3. Suppose gas prices rose to $3.00 per gallon. How would the graph change? Explain.

ANSWER: The line would be steeper because the slope would be 3. It costs more per gallon, so the price of gas goes up faster.

4. Write an equation to represent the situation in number 3.

ANSWER: text annotation indicator y=3x

Direct Variation Assignment

Download the "Direct Variation Assignment" by clicking here. Be sure to work all of the problems on paper. You will use these problems and solutions to complete the "One-Step Equations and Inequalities Homework Quiz 2." Remember you can always go back and review the lessons and videos for more help.

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