The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Which is which
The independent variable is the input - the value you choose (like hours worked). The dependent variable is the output - the value that depends on it (like money earned).
You earn $9 per hour. Identify the variables.
- 1Equation: dollars = 9 × hours.
- 2Hours is independent (you choose it).
- 3Dollars is dependent (it depends on hours).
Why this matters
What you choose vs. what changes because of your choice.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.
Re-reading the question too quickly. Underline what you are solving for before you start calculating.
Key ideas from this lesson
- Which is which
Video walkthroughs
Dependent & Independent Variables
Which quantity you choose and which one depends on it.
Watch on YouTube
Independent & Dependent Variables
Identify input and output in tables and graphs.
Watch on YouTube
What Is a Function?
Relate inputs and outputs to independent and dependent variables.
Watch on YouTube
Graphs of Linear Equations
See how x and y values pair up on a coordinate graph.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfIn the equation d = 5t, which variable is independent and which is dependent?
Step-by-step solution
- 1t is the input you choose (time).
- 2d depends on t (distance), so t is independent and d is dependent.
Exercise 2
Try it yourselfA gym charges $25 per month plus a $10 sign-up fee. Write an equation for total cost C after m months.
Step-by-step solution
- 1$25 per month → 25m.
- 2Plus one-time $10 fee: C = 25m + 10.
Exercise 3
Try it yourselfYou earn $12 per hour. Complete the table: 0 h → $0, 3 h → ?, 5 h → ?
Step-by-step solution
- 1Equation: earnings = 12 × hours.
- 23 hours: 12 × 3 = 36. 5 hours: 12 × 5 = 60.
Exercise 4
Try it yourselfA taxi charges $3 plus $2 per mile. Which is the independent variable in c = 2m + 3?
Step-by-step solution
- 1m represents miles, which you choose.
- 2c (cost) depends on m, so m is independent.
Exercise 5
Try it yourselfA plant grows 2 cm per week. It starts at 5 cm tall. Write an equation for height h after w weeks and find h when w = 6.
Step-by-step solution
- 1h = 2w + 5.
- 2When w = 6: h = 2(6) + 5 = 17 cm.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Independent & Dependent Variables
Question 1 of 5
In y = 4x, x is the dependent variable.