INDEPENDENT VARIABLE
Definition Of Independent Variable
Independent variable is a variable in an equation, whose values make up the domain.
In other words, an independent variable in an equation may have its value freely chosen regardless the values of any other variable.
Video Examples: The Kid-Friendly Definition of Dependent Variables : Algebra
Example of Independent Variable
In the equation y = 7x + 5, the independent variable is x. The variable y is not independent, because it depends on the value chosen for x
Solved Example on Independent Variable
Ques: What is the independent variable in the function?
Choices:
A. f(x)
B. 3/2
C. x
D. no independent variable
Correct Answer: C
Solution:
Step 1: Independent variable is a variable in an equation, whose values make up the domain.
Step 2: So, the independent variable in the given equation is x.
Quick Summary
- The independent variable is the input of a function.
- The value of the independent variable does not depend on any other variable in the equation.
- In a graph, the independent variable is typically plotted on the x-axis.
🍎 Teacher Insights
Use real-world examples to illustrate the concept. For instance, the time spent studying (independent variable) affects the exam score (dependent variable). Emphasize the cause-and-effect relationship.🎓 Prerequisites
- Variables
- Equations
- Domain
- Functions
Check Your Knowledge
Q1: In the equation y = 3x - 2, which variable is independent?
Q2: Which of the following is true about an independent variable?
Frequently Asked Questions
Q: How do I identify the independent variable in an equation?
A: Look for the variable whose value can be chosen freely. It's the input to the function.
Q: Can an equation have more than one independent variable?
A: Yes, in multivariable functions. For example, in z = f(x, y), both x and y are independent variables.