Independent and Dependent Variables in Tables and Graphs

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Independent and Dependent Variables in Tables and Graphs 14.2 Independent and Dependent Variables in Tables and Graphs How can you identify independent and dependent quantities from tables and graphs?

Texas Essential Knowledge and Skills The student is expected to: Expressions, equations, and relationships—6.6.A Identify independent and dependent quantities from tables and graphs. Expressions, equations, and relationships—6.6.C Represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b. Mathematical Processes 6.1.D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Identifying Independent and Dependent Quantities from a Table Many real-world situations involve two variable quantities in which one quantity depends on the other. The quantity that depends on the other quantity is called the dependent variable, and the quantity it depends on is called the independent variable.

What are the two quantities in this situation? Time & distance A freight train moves at a constant speed. The distance y in miles that the train has traveled after x hours is shown in the table. What are the two quantities in this situation? Time & distance Which of these quantities depends on the other? Distance depends on time What is the independent variable? Time, x What is the dependent variable? Distance, y How far does the train travel each hour? 50 miles

Identifying Independent and Dependent Variables from a Graph An art teacher has 20 pounds of clay but wants to buy more clay for her class. The amount of clay x purchased by the teacher and the amount of clay y available for the class are shown on the graph. If the teacher buys 10 more pounds of clay, how many pounds will be available for the art class? 30 lbs. If the art class has a total of 50 pounds of clay available, how many pounds of clay did the teacher buy? How can you use the graph to find this information? 30 lb; find the point on the graph with a y-coordinate of 50. Then find the x-coordinate of this point, which is 30

Describing Relationships Between Independent and Dependent Variables Thinking about how one quantity depends on another helps you identify which quantity is the independent variable and which quantity is the dependent variable. In a graph, the independent variable is usually shown on the horizontal axis and the dependent variable on the vertical axis.

ADDITIONAL EXAMPLE 1 A The table below shows a relationship between two variables, x and y. Describe a possible situation the table could represent. Describe the independent and dependent variables in this situation.

ADDITIONAL EXAMPLE 1 Sample answer: The table could represent the amount a person earns at a rate of $8 per hour. The independent variable, x, is the number of hours the person works. The dependent variable, y, is the total earnings.

ADDITIONAL EXAMPLE 1 B The graph below shows a relationship between two variables, x and y. Describe a possible situation the graph could represent. Describe the independent and dependent variables.

ADDITIONAL EXAMPLE 1 Sample answer: The graph could represent the progress of a rock climber, starting at a 2-foot height and continuing at a pace of 1 foot every second. The independent variable is the number of seconds, and the dependent variable is the total number of feet climbed after x seconds.

14.2 LESSON QUIZ 6.6.A The graph below shows the relationship between the number of tickets Lisa is ordering for a raffle and the cost. Use the graph to answer questions 1–3.

1. What are the dependent and independent variables? Independent variable, x, is the number of tickets bought; dependent variable, y, is the total cost. 2. Is the relationship between the two variables additive or multiplicative? It is an additive relationship

3. Describe the relationship between the two quantities in words. The total cost is the number of tickets bought plus $5 for postage for the tickets.

4. Describe a possible situation that can be represented by the table. Identify the dependent and independent variables in this situation. Sample answer: Parking at the airport costs $7 per day. Independent variable, x, is the number of days a vehicle is parked; dependent variable, y, is the total cost for parking.

Introduce students to independent and dependent variables in situations that involve decimals or fractions. For example: Gina is charged $0.15 for each text message that she sends. 1. What is the independent variable? a a. number of texts sent b. charge per text c. total amount charged for texting

c 2. 3. b = 0.15s What is the dependent variable? a. number of texts sent b. charge per text c. total amount charged for texting 3. Write an equation that expresses the situation. Let b be the amount of Gina’s bill. Let s be the number of texts sent. b = 0.15s

How can you identify independent and dependent quantities from tables and graphs? Sample answer: The dependent variable is the quantity that depends on the other variable. On a graph, the independent variable is shown on the horizontal axis and the dependent variable is shown on the vertical axis.