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In this lesson, we will use variables to represent two quantities in a real-world problem that change in relationship to one another. We will also learn how to write and analyze an equation in terms of **dependent and independent variables**.

**See the fact file below for more information on the dependent and independent variables or alternatively, you can download our 31-page Dependent and Independent Variables worksheet pack to utilise within the classroom or home environment.**

## Key Facts & Information

### VARIABLES

- A variable is a quantity that can change or that may take on different values. This refers to the letter or symbol representing such a quantity in an expression, equation, inequality, or matrix.
- A variable can either be dependent or independent.

### INDEPENDENT VARIABLE

- An independent variable is a variable that represents a quantity that is being manipulated in an experiment.
- x is often the variable used to represent the independent variable in an equation.
- You are working a part-time job to earn your allowance. For each hour, you earn $3. What is the independent variable?
- The independent variable is the number of hours you perform in your part-time job, because this is the variable you have control over.

### DEPENDENT VARIABLE

- A dependent variable represents a quantity whose value depends on how the independent variable is manipulated.
- y is often the variable used to represent the dependent variable in an equation.
- You are working a part-time job to earn your allowance. For each hour, you earn $3. What is the dependent variable?
- The dependent variable is the amount of money you earn, because it depends on how many hours you work.

### SOLVING WORD PROBLEMS

- Example: You are working as a part-time crew member at a fast food chain to earn your allowance. For each hour, you earn $3. In the equation, h is the number of hours you perform, and p is the number of dollars you earn.
- The relationship between these two variables can be expressed by the following equation:
- p = 4h

- The dependent variable is the number that is affected when you change the independent variable – it depends on the independent variable.
- You are earning your allowance based on how many hours you work at your part-time job, so the number of dollars you earn depends on the number of hours you work. Therefore, the dependent variable is the number of dollars you earn from working a part-time job, and the number of hours is the independent variable.
- Example: Your grandmother always has a box of brownies on her counter. One day, while you are visiting, you ate 5 brownies from the box. In the equation below, a is the number of brownies remaining in the box, and b is the number of brownies in the box before your visit.

The relationship between these two variables can be expressed by the following equation:- a = b – 5

- The number of brownies remaining in the box depends on the number of brownies in the box before your visit. Therefore, the number of brownies remaining in the box is the dependent variable, and the number of brownies in the box before your visit is the independent variable.

### TABLES FROM EQUATIONS WITH TWO VARIABLES

- Complete the table for the given rule:
- b = a + 8

- In the equation, a + 8 means 8 is added to a.
- To find each value of b, we need to take each value of a and add 8.
- For example, when a = 2:
- b = 2 + 8
- b = 10

- Complete the table for the given rule:
- c = 3d

- In the equation, 3d means d is multiplied by 3.
- We can substitute 15 for c:
- 15 = 3d

- To find the value of d, divide both sides of the equation by 3.
- To find the value of d, we need to take each value of c and divide it by 3.
- To find the value of c, we need to take each value of d and multiply it by 3.
- For example, when d = 10:
- c = 3 x 10
- c = 30

- Can you complete the rest of the table? Write your solution and answer on a separate sheet of scratch paper.

### RELATIONSHIPS BETWEEN QUANTITIES IN EQUATIONS AND GRAPHS

- Letโs try solving this problem.
- Example: A membership at a yoga studio costs $25 per month. Write an equation for the cost of the membership, a, that you pay if you keep your membership for b months.
- Equation: a = 25b

- How much will your membership cost if you keep it for 24 months?

You pay $25 for each month of your membership. The total cost depends on b, the number of months you are a member. To find the total cost, a, we can use the equation: a = 25b. - To find the cost of the yoga membership for 24 months, we can substitute 24 into the equation for b.
- a = 25b
- a = 25 x 24
- a = 600

- The equation is a = 25b. The yoga membership will cost $600 for 24 months.
- Hereโs another example.
- Example: You buy boxes of blueberries at the market. Each box costs $6. Write an equation for the number of dollars, a, that you spend on b boxes.
- Equation: a = 6b

- You pay $6 for each box of blueberries. The number of dollars you spend depends on b, the number of boxes of blueberries you buy.
- To find the number of dollars you spend on blueberries, we can use the equation: a = 6b.
- Remember, you want to find the number of dollars you will spend if you buy 2 boxes and 5 boxes.
- 12 = 6 x 2
- 30 = 6 x 5

- Now, we can turn the values for b and a from the equation into ordered pairs in the form (x,y). The ordered pairs are: (2, 12) and (5, 30).
- Each x value represents a number on the horizontal axis, and each y value represents a number on the vertical axis.
- Therefore, the equation is a = 6b.

**Dependent and Independent Variables Worksheets**

This is a fantastic bundle which includes everything you need to know about the dependent and independent variables across 31 in-depth pages. These are** ready-to-use Dependent and Independent Variables worksheets that are perfect for teaching students about the variables and how to represent two quantities in a real-world problem that change in relationship to one another. We will also learn how to write and analyze an equation in terms of dependent and independent variables. **

### Complete List Of Included Worksheets

- Lesson Plan
- Dependent and Independent Variables
- Two Variables
- Which Is Which?
- Just a Refresher
- Translating Expressions
- Matching Equations
- Whatโs the Rule?
- Tables From Equations
- Graphs and Equations
- Graphing Names
- Real Wor(l)d Variables

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**Use With Any Curriculum**

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