The graph shows cost in dollars (y) against hours of parking (x). Find k in y = kx and say what the point (1, k) means.

k = 2; 1 hour of parking costs $2.00

The graph shows miles walked (y) against hours walked (x). Find k in y = kx and say what the point (1, k) means.

k = 9/4; 1 hour of walking covers 2.25 miles

The graph shows gallons of water from a hose (y) against minutes (x). Find k in y = kx and say what the point (1, k) means.

k = 9/2; the hose puts out 4.5 gallons in 1 minute

Proportional relationships worksheet

y is proportional to x when y divided by x gives the same number every time. That number is the constant of proportionality, k, and the equation is y = kx. A table where y climbs by a fixed amount but does not start at zero is linear, not proportional.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Proportional Relationships Date Period Answer each question. Decide if the table is proportional $\begin{aligned} Do these values show a proportional relationship? If they do, what is k ? \\ \begin{array}{cc} x & y \\ 12 & 3 \\ 28 & 7 \\ 32 & 8 \\ 40 & 10 \end{array} \end{aligned}$ $\begin{aligned} Could these values come from an equation y = k x ? If they could, find k . \\ \begin{array}{cc} x & y \\ 2 & 8 \\ 4 & 32 \\ 6 & 72 \\ 8 & 128 \end{array} \end{aligned}$ $\begin{aligned} Decide whether y is proportional to x . If so, find k . \\ \begin{array}{cc} x & y \\ 3 & 26 \\ 4 & 36 \\ 6 & 56 \\ 7 & 66 \end{array} \end{aligned}$ $\begin{aligned} Is the ratio y : x the same for every pair? If so, state the constant of proportionality. \\ \begin{array}{ccccc} x & 3 & 5 & 7 & 9 \\ y & 48 & 80 & 112 & 144 \end{array} \end{aligned}$ Find the constant of proportionality $\begin{aligned} These values of x and y are proportional. What is k ? \\ Points: (3, 39), (4, 52), (5, 65), (6, 78) \end{aligned}$ $\begin{aligned} y is proportional to x . Find k . \\ \begin{array}{ccccc} x & 3 & 5 & 7 & 9 \\ y & 30 & 50 & 70 & 90 \end{array} \end{aligned}$ $\begin{aligned} What is the constant of proportionality k in y = k x ? \\ Points: (12, 3), (20, 5), (28, 7), (36, 9) \end{aligned}$ $\begin{aligned} y is proportional to x . Find k . \\ Points: (4, 15), (16, 60), (28, 105), (40, 150) \end{aligned}$ Write $y = kx$ from the table $\begin{aligned} Write the equation for the table. \\ \begin{array}{ccccc} x & 12 & 18 & 21 & 30 \\ y & 28 & 42 & 49 & 70 \end{array} \end{aligned}$ $\begin{aligned} Use the constant of proportionality to write the equation in the form y = k x . \\ \begin{array}{ccccc} x & 10 & 30 & 35 & 45 \\ y & 2 & 6 & 7 & 9 \end{array} \end{aligned}$ $\begin{aligned} Write the equation for the table. \\ \begin{array}{cc} x & y \\ 2 & 7 \\ 8 & 28 \\ 12 & 42 \\ 14 & 49 \end{array} \end{aligned}$ Decide if the graph is proportional Tell whether $x$ and $y$ are proportional in this graph. If they are, write the constant of proportionality $k$ . Is $y$ proportional to $x$ ? If so, find the constant of proportionality $k$ . Decide whether $y$ is proportional to $x$ . If it is, state the constant of proportionality $k$ . Find and interpret $k$ from the graph The graph shows cost in dollars ( $y$ ) against hours of parking ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. The graph shows miles walked ( $y$ ) against hours walked ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. The graph shows gallons of water from a hose ( $y$ ) against minutes ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. Write $y = kx$ from a description Lena reads 2 pages a day. Write an equation for the pages $y$ read in $x$ days. Sam earns $23 per hour. Write an equation for the pay $y$ for $x$ hours. Tickets cost $8 each. Write an equation for the total cost $y$ of $x$ tickets. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Proportional Relationships

Date Period

Answer each question.

Decide if the table is proportional
$\begin{aligned} Do these values show a proportional relationship? If they do, what is k ? \\ \begin{array}{cc} x & y \\ 12 & 3 \\ 28 & 7 \\ 32 & 8 \\ 40 & 10 \end{array} \end{aligned}$
$\begin{aligned} Could these values come from an equation y = k x ? If they could, find k . \\ \begin{array}{cc} x & y \\ 2 & 8 \\ 4 & 32 \\ 6 & 72 \\ 8 & 128 \end{array} \end{aligned}$
$\begin{aligned} Decide whether y is proportional to x . If so, find k . \\ \begin{array}{cc} x & y \\ 3 & 26 \\ 4 & 36 \\ 6 & 56 \\ 7 & 66 \end{array} \end{aligned}$
$\begin{aligned} Is the ratio y : x the same for every pair? If so, state the constant of proportionality. \\ \begin{array}{ccccc} x & 3 & 5 & 7 & 9 \\ y & 48 & 80 & 112 & 144 \end{array} \end{aligned}$

Find the constant of proportionality
$\begin{aligned} These values of x and y are proportional. What is k ? \\ Points: (3, 39), (4, 52), (5, 65), (6, 78) \end{aligned}$
$\begin{aligned} y is proportional to x . Find k . \\ \begin{array}{ccccc} x & 3 & 5 & 7 & 9 \\ y & 30 & 50 & 70 & 90 \end{array} \end{aligned}$
$\begin{aligned} What is the constant of proportionality k in y = k x ? \\ Points: (12, 3), (20, 5), (28, 7), (36, 9) \end{aligned}$
$\begin{aligned} y is proportional to x . Find k . \\ Points: (4, 15), (16, 60), (28, 105), (40, 150) \end{aligned}$

Write $y = kx$ from the table
$\begin{aligned} Write the equation for the table. \\ \begin{array}{ccccc} x & 12 & 18 & 21 & 30 \\ y & 28 & 42 & 49 & 70 \end{array} \end{aligned}$
$\begin{aligned} Use the constant of proportionality to write the equation in the form y = k x . \\ \begin{array}{ccccc} x & 10 & 30 & 35 & 45 \\ y & 2 & 6 & 7 & 9 \end{array} \end{aligned}$
$\begin{aligned} Write the equation for the table. \\ \begin{array}{cc} x & y \\ 2 & 7 \\ 8 & 28 \\ 12 & 42 \\ 14 & 49 \end{array} \end{aligned}$

Decide if the graph is proportional
Tell whether $x$ and $y$ are proportional in this graph. If they are, write the constant of proportionality $k$ .
Is $y$ proportional to $x$ ? If so, find the constant of proportionality $k$ .
Decide whether $y$ is proportional to $x$ . If it is, state the constant of proportionality $k$ .

Find and interpret $k$ from the graph
The graph shows cost in dollars ( $y$ ) against hours of parking ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means.
The graph shows miles walked ( $y$ ) against hours walked ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means.
The graph shows gallons of water from a hose ( $y$ ) against minutes ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means.

Write $y = kx$ from a description
Lena reads 2 pages a day. Write an equation for the pages $y$ read in $x$ days.
Sam earns $23 per hour. Write an equation for the pay $y$ for $x$ hours.
Tickets cost $8 each. Write an equation for the total cost $y$ of $x$ tickets.



Sigma Prep · sigmaprep.io/worksheets Name Proportional RelationshipsAnswer keyVersion 1 Date Period Answer each question. Decide if the table is proportional $\begin{aligned} Do these values show a proportional relationship? If they do, what is k ? \\ \begin{array}{cc} x & y \\ 12 & 3 \\ 28 & 7 \\ 32 & 8 \\ 40 & 10 \end{array} \end{aligned}$ Yes, $k = \frac{1}{4}$ $\begin{aligned} Could these values come from an equation y = k x ? If they could, find k . \\ \begin{array}{cc} x & y \\ 2 & 8 \\ 4 & 32 \\ 6 & 72 \\ 8 & 128 \end{array} \end{aligned}$ No $\begin{aligned} Decide whether y is proportional to x . If so, find k . \\ \begin{array}{cc} x & y \\ 3 & 26 \\ 4 & 36 \\ 6 & 56 \\ 7 & 66 \end{array} \end{aligned}$ No $\begin{aligned} Is the ratio y : x the same for every pair? If so, state the constant of proportionality. \\ \begin{array}{ccccc} x & 3 & 5 & 7 & 9 \\ y & 48 & 80 & 112 & 144 \end{array} \end{aligned}$ Yes, $k = 16$ Find the constant of proportionality $\begin{aligned} These values of x and y are proportional. What is k ? \\ Points: (3, 39), (4, 52), (5, 65), (6, 78) \end{aligned}$ $k = 13$ $\begin{aligned} y is proportional to x . Find k . \\ \begin{array}{ccccc} x & 3 & 5 & 7 & 9 \\ y & 30 & 50 & 70 & 90 \end{array} \end{aligned}$ $k = 10$ $\begin{aligned} What is the constant of proportionality k in y = k x ? \\ Points: (12, 3), (20, 5), (28, 7), (36, 9) \end{aligned}$ $k = \frac{1}{4}$ $\begin{aligned} y is proportional to x . Find k . \\ Points: (4, 15), (16, 60), (28, 105), (40, 150) \end{aligned}$ $k = \frac{15}{4}$ Write $y = kx$ from the table $\begin{aligned} Write the equation for the table. \\ \begin{array}{ccccc} x & 12 & 18 & 21 & 30 \\ y & 28 & 42 & 49 & 70 \end{array} \end{aligned}$ $y = \frac{7}{3} x$ $\begin{aligned} Use the constant of proportionality to write the equation in the form y = k x . \\ \begin{array}{ccccc} x & 10 & 30 & 35 & 45 \\ y & 2 & 6 & 7 & 9 \end{array} \end{aligned}$ $y = \frac{1}{5} x$ $\begin{aligned} Write the equation for the table. \\ \begin{array}{cc} x & y \\ 2 & 7 \\ 8 & 28 \\ 12 & 42 \\ 14 & 49 \end{array} \end{aligned}$ $y = \frac{7}{2} x$ Decide if the graph is proportional Tell whether $x$ and $y$ are proportional in this graph. If they are, write the constant of proportionality $k$ .No Is $y$ proportional to $x$ ? If so, find the constant of proportionality $k$ .Yes, $k = 3$ Decide whether $y$ is proportional to $x$ . If it is, state the constant of proportionality $k$ .Yes, $k = \frac{1}{3}$ Find and interpret $k$ from the graph The graph shows cost in dollars ( $y$ ) against hours of parking ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. $k = 2$ ; 1 hour of parking costs $2.00 The graph shows miles walked ( $y$ ) against hours walked ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. $k = \frac{9}{4}$ ; 1 hour of walking covers 2.25 miles The graph shows gallons of water from a hose ( $y$ ) against minutes ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. $k = \frac{9}{2}$ ; the hose puts out 4.5 gallons in 1 minute Write $y = kx$ from a description Lena reads 2 pages a day. Write an equation for the pages $y$ read in $x$ days. $y = 2 x$ Sam earns $23 per hour. Write an equation for the pay $y$ for $x$ hours. $y = 23 x$ Tickets cost $8 each. Write an equation for the total cost $y$ of $x$ tickets. $y = 8 x$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Proportional RelationshipsAnswer keyVersion 1

Date Period

Answer each question.

Decide if the table is proportional
$\begin{aligned} Do these values show a proportional relationship? If they do, what is k ? \\ \begin{array}{cc} x & y \\ 12 & 3 \\ 28 & 7 \\ 32 & 8 \\ 40 & 10 \end{array} \end{aligned}$ Yes, $k = \frac{1}{4}$
$\begin{aligned} Could these values come from an equation y = k x ? If they could, find k . \\ \begin{array}{cc} x & y \\ 2 & 8 \\ 4 & 32 \\ 6 & 72 \\ 8 & 128 \end{array} \end{aligned}$ No
$\begin{aligned} Decide whether y is proportional to x . If so, find k . \\ \begin{array}{cc} x & y \\ 3 & 26 \\ 4 & 36 \\ 6 & 56 \\ 7 & 66 \end{array} \end{aligned}$ No
$\begin{aligned} Is the ratio y : x the same for every pair? If so, state the constant of proportionality. \\ \begin{array}{ccccc} x & 3 & 5 & 7 & 9 \\ y & 48 & 80 & 112 & 144 \end{array} \end{aligned}$ Yes, $k = 16$

Find the constant of proportionality
$\begin{aligned} These values of x and y are proportional. What is k ? \\ Points: (3, 39), (4, 52), (5, 65), (6, 78) \end{aligned}$ $k = 13$
$\begin{aligned} y is proportional to x . Find k . \\ \begin{array}{ccccc} x & 3 & 5 & 7 & 9 \\ y & 30 & 50 & 70 & 90 \end{array} \end{aligned}$ $k = 10$
$\begin{aligned} What is the constant of proportionality k in y = k x ? \\ Points: (12, 3), (20, 5), (28, 7), (36, 9) \end{aligned}$ $k = \frac{1}{4}$
$\begin{aligned} y is proportional to x . Find k . \\ Points: (4, 15), (16, 60), (28, 105), (40, 150) \end{aligned}$ $k = \frac{15}{4}$

Write $y = kx$ from the table
$\begin{aligned} Write the equation for the table. \\ \begin{array}{ccccc} x & 12 & 18 & 21 & 30 \\ y & 28 & 42 & 49 & 70 \end{array} \end{aligned}$ $y = \frac{7}{3} x$
$\begin{aligned} Use the constant of proportionality to write the equation in the form y = k x . \\ \begin{array}{ccccc} x & 10 & 30 & 35 & 45 \\ y & 2 & 6 & 7 & 9 \end{array} \end{aligned}$ $y = \frac{1}{5} x$
$\begin{aligned} Write the equation for the table. \\ \begin{array}{cc} x & y \\ 2 & 7 \\ 8 & 28 \\ 12 & 42 \\ 14 & 49 \end{array} \end{aligned}$ $y = \frac{7}{2} x$

Decide if the graph is proportional
Tell whether $x$ and $y$ are proportional in this graph. If they are, write the constant of proportionality $k$ .No
Is $y$ proportional to $x$ ? If so, find the constant of proportionality $k$ .Yes, $k = 3$
Decide whether $y$ is proportional to $x$ . If it is, state the constant of proportionality $k$ .Yes, $k = \frac{1}{3}$

Find and interpret $k$ from the graph
The graph shows cost in dollars ( $y$ ) against hours of parking ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. $k = 2$ ; 1 hour of parking costs $2.00
The graph shows miles walked ( $y$ ) against hours walked ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. $k = \frac{9}{4}$ ; 1 hour of walking covers 2.25 miles
The graph shows gallons of water from a hose ( $y$ ) against minutes ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. $k = \frac{9}{2}$ ; the hose puts out 4.5 gallons in 1 minute

Write $y = kx$ from a description
Lena reads 2 pages a day. Write an equation for the pages $y$ read in $x$ days. $y = 2 x$
Sam earns $23 per hour. Write an equation for the pay $y$ for $x$ hours. $y = 23 x$
Tickets cost $8 each. Write an equation for the total cost $y$ of $x$ tickets. $y = 8 x$

How to do these

Find the constant of proportionality $\begin{array}{cccc} x & 2 & 4 & 6 \\ y & 6 & 12 & 18 \end{array}$

Divide y by x in any column.
6 over 2 is 3, and 12 over 4 is 3 as well.

The answer is $k = 3$ .

Where students go wrong

Testing one column and stopping. One pair always divides to something; proportional means every pair divides to the same thing.

Also called constant of proportionality, y = kx, proportional tables or direct proportion.

What you can put on this worksheet

Proportional or not, from a table: Do these values show a proportional relationship? If they do, what is $k$ ?
$\begin{array}{cc} x & y \\ 1 & 5 \\ 5 & 25 \\ 6 & 30 \\ 8 & 40 \end{array}$ → Yes, $k = 5$
The constant of proportionality: These values of $x$ and $y$ are proportional. What is $k$ ?
$\begin{array}{ccccc} x & 1 & 5 & 6 & 8 \\ y & 5 & 25 & 30 & 40 \end{array}$ → $k = 5$
The equation y = kx from a table: Use the constant of proportionality to write the equation in the form $y = k x$ .
$\begin{array}{ccccc} x & 1 & 5 & 6 & 8 \\ y & 5 & 25 & 30 & 40 \end{array}$ → $y = 5 x$
Proportional or not, from a graph: Tell whether $x$ and $y$ are proportional in this graph. If they are, write the constant of proportionality $k$ . → No
k from a graph, and what (1, k) means: The graph shows miles walked ( $y$ ) against hours walked ( $x$ ). Find $k$ in $y = k x$ and say what the point $(1, k)$ means. → $k = 3$ ; 1 hour of walking covers 3 miles
y = kx from a description: Sam earns $21 per hour. Write an equation for the pay $y$ for $x$ hours. → $y = 21 x$

Questions about these worksheets

Yes. Every proportional relationships sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the proportional relationships questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 6: proportional or not, from a table, the constant of proportionality, the equation y = kx from a table, proportional or not, from a graph, k from a graph, and what (1, k) means and y = kx from a description. Tick as many as you want and set how many of each, or let it spread them evenly.

Testing one column and stopping. One pair always divides to something; proportional means every pair divides to the same thing.

Proportional relationships worksheet

Select your difficulty

Decide if the table is proportional

Find the constant of proportionality

Write y=kxy = kxy=kx from the table

Decide if the graph is proportional

Find and interpret kkk from the graph

Write y=kxy = kxy=kx from a description

Decide if the table is proportional

Find the constant of proportionality

Write y=kxy = kxy=kx from the table

Decide if the graph is proportional

Find and interpret kkk from the graph

Write y=kxy = kxy=kx from a description

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these proportional relationships worksheets free?+

Do the proportional relationships worksheets come with an answer key?+

Are these proportional relationships worksheets printable?+

What grade are these proportional relationships worksheets for?+

Can I get a different version of the same proportional relationships worksheet?+

Is this a free alternative to Kuta Software for proportional relationships?+

Can I choose how hard the proportional relationships questions are?+

What kinds of question are on a proportional relationships worksheet?+

What do students get wrong with proportional relationships?+

Write $y = kx$ from the table

Find and interpret $k$ from the graph

Write $y = kx$ from a description

Write $y = kx$ from the table

Find and interpret $k$ from the graph

Write $y = kx$ from a description