DEPENDENT VARIABLE

Dependent Variable

Definition Of Dependent Variable

Dependent Variable is a variable whose value depends on the values of one or more independent variables.

Example of Denominator

In p = 4q, p is the dependent variable, because its value depends on the value of q.
In z = 3x² - 2y³, z is the dependent variable.

Video Examples: The Kid-Friendly Definition of Dependent Variables : Algebra

Solved Example on Dependent Variable

Ques: What is the dependent variable in the function f(x) = 3 - x?

Choices:

A. no dependent variable
B. 3
C. f(x)
D. x
Correct Answer: C

Solution:

Step 1: In the function f(x) = 3 - x, the value of f(x) depends on the value of x. So, f(x) is the dependent variable.

Quick Summary

The dependent variable's value is determined by the independent variable.
In an equation, it is the 'output' or result of the function.

\[ y = f(x) (where y is the dependent variable) \]

⚠️ Common Mistakes

Confusing the dependent variable with the independent variable.
Assuming a variable is independent without considering the context of the equation.

🌍 Real-World Uses

In a scientific experiment, the amount of plant growth (dependent variable) depends on the amount of fertilizer used (independent variable).
The cost of a taxi ride (dependent variable) depends on the distance traveled (independent variable).
A student's exam score (dependent variable) depends on the amount of time they spent studying (independent variable).

📋 Standards Alignment

CCSS.MATH.CONTENT.HSA.REI.A.1
CCSS.MATH.CONTENT.HSA.REI.C.6

🍎 Teacher Insights

Use real-world examples to illustrate the concept, such as the amount of plant growth (dependent) depending on the amount of water (independent).

🎓 Prerequisites

Variables
Independent Variables
Functions

Check Your Knowledge

Q1: In the function g(t) = 5t + 2, which is the dependent variable?

A. t B. 5 C. 2 D. g(t)

Q2: Which of the following best describes a dependent variable?

A. A variable that is changed in an experiment B. A variable that is not affected by other variables C. A variable whose value depends on other variables D. A constant value

Frequently Asked Questions

Q: How do I identify the dependent variable in an equation?
A: Look for the variable that is being 'solved for' or is expressed in terms of other variables. It is the output of the function.

Q: Can a variable be both dependent and independent?
A: Yes, in more complex models or systems, a variable can be dependent in one equation and independent in another. It depends on the relationship being modeled.