7.RP.2: Recognize Proportional Relationships
Also written as 7.RP.A.2 and CCSS.MATH.CONTENT.7.RP.A.2 · Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Official Wording
Recognize and represent proportional relationships between quantities.
Common Core State Standards, Grade 7, Ratios & Proportional Relationships · Read it at the source · Checked October 14, 2026
What 7.RP.2 Means in Plain English
Seventh graders test whether two quantities are proportional: every pair in a table gives the same ratio, or the graph is a straight line through (0, 0). Three notebooks cost $4.50 and six cost $9.00, so the constant of proportionality is 1.50 and the equation is c = 1.5n.
They also read points: on the graph of c = 1.5n, (1, 1.5) is the unit rate and (0, 0) says zero notebooks cost nothing. In 8th grade the constant becomes the slope of a line (8.EE.5) and proportional relationships become one kind of function (8.F.4).
7.RP.2 I Can Statements
- I can tell from a table or graph whether a relationship is proportional.
- I can find the constant of proportionality in a table, graph or equation.
- I can explain what the points (0, 0) and (1, r) mean.
7.RP.2 Worked Example
One table of prices and the four questions the standard asks of it: is it proportional, what is the constant, what is the equation, and what does a point mean.
A store sells 2 notebooks for $3.00, 5 for $7.50 and 8 for $12.00. Is the cost proportional to the number of notebooks? If so, write the equation and explain what the point (1, 1.50) means.
- Part a: test the ratios. Divide cost by notebooks in every row. If every quotient matches, the relationship is proportional.3.00 ÷ 2 = 1.50, 7.50 ÷ 5 = 1.50, 12.00 ÷ 8 = 1.50
- Part b: the shared quotient is the constant of proportionality, the cost of one notebook.k = 1.50
- Part c: cost equals the constant times the number of notebooks. Choose letters and write it.c = 1.50n
- Part d: a point (x, y) is (notebooks, cost). (1, 1.50) means 1 notebook costs $1.50, the unit rate. (0, 0) means no notebooks, no cost.(1, 1.50): one notebook costs $1.50
- Plot the three rows and they fall on one straight line through (0, 0), which is the graphing test from part a.(2, 3), (5, 7.5) and (8, 12) line up through the origin
Check it: Substitute a row into the equation: n = 8 gives c = 1.50 × 8 = 12.00, the price in the table. A table like 2 for $3.00 and 5 for $8.00 would have failed step 1 (1.50 against 1.60).
Common Mistakes with 7.RP.2
Calling any straight line proportional
A gym charges $20 to join plus $10 a month, so cost is proportional to months
Try this: Check the origin: 0 months would cost $20, not $0, so the line misses (0, 0) and the relationship is not proportional.
Testing one row only
2 for $3 and 5 for $8: 3 ÷ 2 = 1.5, so k = 1.5
Try this: Divide every row. 8 ÷ 5 = 1.6, which breaks the pattern, and one mismatch is enough to say not proportional.
Dividing the wrong way round
k = 2 ÷ 3.00, so c = 0.67n
Try this: Match the division to the question: cost per notebook is cost divided by notebooks, and the equation must give $3.00 when n = 2.
Where 7.RP.2 Fits
Practice 7.RP.2
Quick Check
- A table shows 3 pounds of apples for $4.50 and 7 pounds for $10.50. Is the cost proportional to the weight? What is k?
- Write an equation for the total cost t of n tickets at $8 each. What does (0, 0) mean on its graph?
- The graph of a proportional relationship passes through (4, 10). What is the unit rate, and which point shows it?