The lesson
This lesson teaches Independent & Dependent Variables. 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).
When you study which is which, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
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
Independent & Dependent Variables shows up constantly in what you choose vs. what changes because of your choice. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- Which is which
Video walkthrough
Dependent & Independent Variables
Which quantity you choose and which one depends on it.
Watch on YouTubeIndependent & Dependent Variables
Identify input and output in tables and graphs.
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.