Dependent and Independent Variables

1. Dependent and Independent Variables

2. Variables • Something that varies. • Specifically, variables represent persons or objects that can be manipulated, controlled. • Variation: How much a variable varies. • Those with little variation are called constants.

3. Variables Cont. • Two variables are often related in real-world situations. • Example: The sale of ice cream cones may be related to the temperature outside. • The two variables are: • number of ice creams sold • the temperature outside

4. Examples of Variables

5. Independent Variables • a variable whose value does NOT depend on another variable. • Located in the x column (left side)of a table, and fall on the x axis. • There can only be one independent variable • Example: Quality rating of peanut butter

6. Dependent Variables • a variable whose value depends on another variable. • Located in the y column (right side) of a table, and fall on the y axis. • There can be any number of dependent variables. • Example: Price of peanut butter.

7. You can use tables, graphs, and equations to represent relationships between independent and dependent variables.

8. Identifying Variables in Tables • The table shows the relationship between temperature,t, and the number of ice creams sold,n, throughout the year. Can you see the relationship in the table? Which is the dependent variable? The number of ice creams sold Which is the independent variable? Temperature

9. Identifying Variables in Equations • The equation c=5n represents the relationship between the total amount of money collected,c, if the cost of a ticket to the Valentine dance is $5.00 each. What is the relationship between the variables? The more tickets sold, the more money is collected. Which is the dependent variable? The total amount collected Which is the independent variable? The number of tickets sold

10. Identifying Variables in Graphs • The graph represents the relationship between the number of hours,h, Sarah works and the number of dollars,d, she earns. Dollars Earned (d) Sarah’s Earnings What is the relationship between the variables? The more hours worked, the more money earned. Which is the dependent variable? The total amount earned Which is the independent variable? The number of hours worked Hours Worked (h)

11. Identify the independent and dependent variables in the situation. A painter must measure a room before deciding how much paint to buy. The amount of paintdependson the measurement of a room. Dependent: amount of paint Independent: measurement of the room

12. Identify the independent and dependent variables in the situation. A veterinarian must weight an animal before determining the amount of medication. The amount of medicationdepends on the weight of an animal. Dependent: amount of medication Independent: weight of animal

13. Identify the independent and dependent variable in the situation. A company charges $10 per hour to rent a jackhammer. The cost to rent a jackhammerdependson the length of time it is rented. Dependent variable: cost Independent variable: time

14. Identify the independent and dependent variable in the situation. Camronbuys p pounds of apples at $0.99 per pound. The cost of applesdepends on the number of pounds bought. Dependent variable: cost Independent variable: pounds