6.EE.9: Dependent and Independent Variables
Also written as 6.EE.C.9 and CCSS.MATH.CONTENT.6.EE.C.9 · Cluster: Represent and analyze quantitative relationships between dependent and independent variables.
The Official Wording
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Common Core State Standards, Grade 6, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 6.EE.9 Means in Plain English
Sixth graders name two quantities that change together and say which depends on which. A pool fills at 12 gallons a minute, so water w depends on time t: w = 12t. They tabulate (1, 12), (2, 24), (3, 36), plot the points and see one relationship three ways.
This is the first time an equation has two letters and describes a pattern instead of hiding one answer. It grows out of the ratio tables in 6.RP.3 and leads to proportional relationships and the constant of proportionality in 7th grade (7.RP.2), then functions in 8th (8.F.1).
6.EE.9 I Can Statements
- I can say which variable depends on the other in a situation.
- I can write an equation like d = 65t for two changing quantities.
- I can match a table, a graph and an equation to each other.
6.EE.9 Worked Example
A babysitting rate turned into an equation, a table and a graph, with the dependent variable chosen on purpose.
Priya earns $9 an hour babysitting. Write an equation for her earnings, make a table, and describe the graph.
- Decide which quantity depends on which. The hours are chosen first, so hours h is the independent variable and earnings e depends on it.Independent: h (hours). Dependent: e (dollars)
- Write the dependent variable in terms of the independent one. Every hour adds 9 dollars.e = 9h
- Build a table by substituting hours. The independent variable goes in the first column.h: 1, 2, 3, 4 and e: 9, 18, 27, 36
- Plot the pairs with h across and e up: (1, 9), (2, 18), (3, 27), (4, 36). They line up, and each step right is a step of 9 up.Points on a straight line through (0, 0)
- Read the relationship back from all three. In the table e is always 9 times h, on the graph the line rises 9 per hour, and the equation says so directly.e = 9h in table, graph and equation
Check it: Test a pair that is not in the table: 6 hours should pay 6 × 9 = 54, and (6, 54) lands on the same line.
Common Mistakes with 6.EE.9
Swapping the dependent and independent variables
h = 9e, “hours equal nine times earnings”
Try this: Ask which one you choose and which one follows. Hours are chosen, earnings follow, so earnings are written in terms of hours.
Adding instead of multiplying
d = 65t written as d = 65 + t, since “65 and t go together”
Try this: Check the equation against the table: 2 hours at 65 miles per hour is 130, and 65 + 2 is 67. Only multiplication fits.
Plotting the pairs backwards
(9, 1), (18, 2), (27, 3) on the graph of e = 9h
Try this: Label the axes before plotting: independent variable along the bottom, dependent variable up the side, so each pair reads (h, e).
Where 6.EE.9 Fits
Practice 6.EE.9
Quick Check
- A car travels at 55 miles per hour. Write an equation for distance d after t hours, and find d when t = 4.
- In “the cost c of n notebooks at $3 each,” which variable is independent?
- A table shows (1, 7), (2, 14), (3, 21), (4, 28). Write the equation and give the next pair.