# Dependent and Independent Variables (Grade 6)

These lessons, with videos, examples and solutions help Grade 6 students learn how to use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.

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Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Common Core: 6.EE.9

### Suggested Learning Targets

• I can use variables to represent quantities that change in relation to one another
• I can use functions and graph ordered pairs resulting from the function. I can define independent and dependent variables .
• I can use variables to represent two quantities in a real-world problem that change in relationship to one another.
• I can write an equation to express one quantity (dependent) in terms of the other quantity (independent).
• I can analyze the relationship between the dependent variable and independent variable using tables and graphs.
• I can relate the data in a graph and table to the corresponding equation.

Identify Independent Variable and Dependent Variable on Various Representational Modes
Create equations and inequalities in one variable and use them to solve problems.

1. Jordan squeezes 6 oranges to get 2 1/2 cups of orange juice. Identify the independent variable and dependent variable.

2. Jessica has a summer job that pays \$6.50 per hour. Her total pay for one day was \$32.50. Identify the independent and dependent variables and then graph.

Independent and Dependent Variables

Dependent and independent variables exercise

Example:
On your math quiz, you earn 5 points for each question that you answered correctly. In the table above, q represents the number question that you answer correctly on your math quiz and p represents the total number of points that you score on your quiz. The relationship between these two variables can be expressed by the following equation:
p = 5q
Which of the following statements are true?

Dependent and independent variables exercise

Example:
On your math quiz, you earn 5 points for each question that you answered correctly. In the table above, x represents the number question that you answer correctly on your math quiz and y represents the total number of points that you score on your quiz. The relationship between these two variables can be expressed by the following equation:
y = 5x
Graph the equation.

Dependent and independent variables exercise

Example:
You are buying a gym membership. The membership cost forty dollars per month.
In the graph and table above, d is the number total number of dollars that you pay for your gym membership, and t is the time (in months) that you keep the membership.
Write an equation for the amount of money, d, that you pay for your gym membership if you keep your membership for t months.

The following activities are obtained from Howard County Public School System.

Activities:

Let x = the number of songs downloaded and let y = the total amount of money spent.
Write an equation to show the total amount of money Sally spent during her first month of membership.

Complete the table of values below using your equation.

 x y 0 1 2 3 4 5

Graph your equation on graph paper.
Describe the relationship between x and y. 2. The table shows the relationship between the number of pineapples bought and the total cost.

 Number Bought Total Cost 10 \$25 15 \$37.50 20 \$50 30 \$75

Write an expression to find the total cost of buying any number of pineapples. Use data from the chart to justify your solution.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 