Find k from the plotted points.
k = ___
Graph to constant of proportionality · grades 6–7
Find Unit Rate from a Proportional Graph
Read the constant of proportionality directly from a graph. Exact plotted points make it possible to compare y/x or use the meaningful point (1, k) without estimating from a picture.
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Find Unit Rate from Graphs
Graph to unit rate · Small whole numbers · Seed 261501
Find k from the plotted points.
k = ___
Find k from the plotted points.
k = ___
Find k from the plotted points.
k = ___
Find k from the plotted points.
k = ___
Find k from the plotted points.
k = ___
Find k from the plotted points.
k = ___
Find k from the plotted points.
k = ___
Find k from the plotted points.
k = ___
Find k from the plotted points.
k = ___
No fake precision: tables, graph points, equations, and double number lines come from the same exact whole-number constant of proportionality. Better Buy problems compare integer cents per item, so a winner is never chosen from a rounded display value.
Reading the unit rate from a proportional graph
On the graph of a proportional relationship the unit rate k is the y-value at x = 1, the point (1, k). You can also divide y by x at any plotted point. The line has to pass through the origin and every point has to give the same quotient. If the points do not share one y ÷ x value, the relationship is not proportional and there is no single k.
Worked examples
- A plotted point at (4, 20): k = 20 ÷ 4 = 5. The same line should pass through (1, 5).
- Points (2, 6) and (3, 9): 6 ÷ 2 = 3 and 9 ÷ 3 = 3, so k = 3.
- Not proportional: points (1, 4) and (2, 6) give 4 ÷ 1 = 4 and 6 ÷ 2 = 3. The quotients differ, so there is no single constant.
Common slips
- Reading the y-value at a point where x is not 1 and calling it k. At (4, 20) the unit rate is 5, not 20.
- Counting grid squares instead of reading the labeled scale. If the y-axis counts by 5s, one square is worth 5.
- Assuming any straight line shows a constant of proportionality. The line must also pass through (0, 0).
How to use this worksheet
Ask students to circle the point they used and write the division beside it, then to check a second point. The answer key gives k and the unit-rate point so students can see both ways of reading the graph.
Common Core connection
- 7.RP.A.2.b · Identify the constant of proportionality in tables, graphs, equations, and verbal descriptions.
- 7.RP.A.2.d · Explain what points on a proportional graph mean in the quantities represented.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Note 1
Choose a plotted point and calculate y/x to find k.
Note 2
The point (1, k) shows the y-value for one x-unit, which is the unit rate.
Note 3
If the points do not fall on one straight line through the origin, the relationship is not proportional and has no single k.
Note 4
A line through the origin is necessary but not enough; its y/x value must match every plotted point.
Move among tables, equations, graphs, double number lines, and Better Buy decisions in one exact generator.
Return to ratio foundations →Practice simplified ratios, equivalent tables, unit rates, proportions, and percent proportions.
More skills in this set
Quick answers
Why are points shown instead of only a line?
Visible integer-coordinate points let students read an exact rate rather than estimate a slope from the picture.
Is this the same as slope?
For y = kx, the constant of proportionality equals the slope, but this worksheet emphasizes the per-one rate meaning.
Which standard does this practice?
CCSS 7.RP.A.2b and 7.RP.A.2d: find the constant of proportionality from a graph and explain the meaning of the point (1, r).
Why does the standard single out the point (1, r)?
Because reading it off the graph gives the unit rate directly, tying the picture to the 'per one' meaning students already know from tables.