A plant is 59 centimeters tall and grows 2 centimeters a week. In y = 2x + 59, what does 2 mean?

For each extra week, its height goes up by 2 centimeters

A gym charges $20 to join and $35 per month. In y = 35x + 20, what does 35 mean?

For each extra month, the total paid goes up by $35

A tank starts with 52 gallons of water and fills at 6 gallons per minute. In y = 6x + 52, what does 6 mean?

For each extra minute, the amount of water in the tank goes up by 6 gallons

A plumber charges $85 for a visit plus $105 per hour. In y = 105x + 85, what does 105 mean?

For each extra hour, the total cost goes up by $105

A tank starts with 27 gallons of water and fills at 3 gallons per minute. In y = 3x + 27, what does 3 mean?

For each extra minute, the amount of water in the tank goes up by 3 gallons

A plumber charges $100 for a visit plus $85 per hour. In y = 85x + 100, what does 85 mean?

For each extra hour, the total cost goes up by $85

A gym charges $30 to join and $45 per month. In y = 45x + 30, what does 45 mean?

For each extra month, the total paid goes up by $45

A plant is 50 centimeters tall and grows 9 centimeters a week. In y = 9x + 50, what does 9 mean?

For each extra week, its height goes up by 9 centimeters

A tank starts with 14 gallons of water and fills at 12 gallons per minute. In y = 12x + 14, what does 12 mean?

For each extra minute, the amount of water in the tank goes up by 12 gallons

Worksheets · Pre-Algebra

Linear functions in context worksheet for Pre-Algebra

Pre-Algebra reads linear functions from tables and real situations: the rate of change is how much y grows each time x goes up by 1, and the initial value is y when x is 0. Other questions ask for the equation from a description, or what the rate means in context.

Also taught in Algebra 1, at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Writing Linear Equations (Pre-Algebra). Slope-intercept, point-slope and standard form.
Graphing Linear Equations (Pre-Algebra). A grid on every question.
Slope and Linear Equations (Algebra 1). Slope from two points, and the equation of the line.
Point-Slope Form (Algebra 1). A point and a slope, copied into their places.
Standard Form of a Line (Algebra 1). Ax + By = C, with A positive and whole.

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 Linear Functions in Context Date Period Answer each question. Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 23 & 43 & 63 & 83 \end{array}$ A plumber charges $90 for a visit plus $75 per hour. Write an equation for the total cost, $y$ , after $x$ hours. A plant is 40 centimeters tall and grows 5 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. A plant is 59 centimeters tall and grows 2 centimeters a week. In $y = 2 x + 59$ , what does 2 mean? A gym charges $20 to join and $35 per month. In $y = 35 x + 20$ , what does 35 mean? A tank starts with 52 gallons of water and fills at 6 gallons per minute. In $y = 6 x + 52$ , what does 6 mean? A tank starts with 26 gallons of water and fills at 12 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. A plumber charges $85 for a visit plus $105 per hour. In $y = 105 x + 85$ , what does 105 mean? A gym charges $30 to join and $55 per month. Write an equation for the total paid, $y$ , after $x$ months. Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 1 & 2 & 3 \\ y & 17 & 20 & 23 & 26 \end{array}$ A gym charges $25 to join and $25 per month. Write an equation for the total paid, $y$ , after $x$ months. A tank starts with 27 gallons of water and fills at 3 gallons per minute. In $y = 3 x + 27$ , what does 3 mean? A plumber charges $100 for a visit plus $85 per hour. In $y = 85 x + 100$ , what does 85 mean? A gym charges $30 to join and $45 per month. In $y = 45 x + 30$ , what does 45 mean? A plumber charges $100 for a visit plus $70 per hour. Write an equation for the total cost, $y$ , after $x$ hours. A plant is 23 centimeters tall and grows 2 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. A tank starts with 10 gallons of water and fills at 3 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. A plant is 50 centimeters tall and grows 9 centimeters a week. In $y = 9 x + 50$ , what does 9 mean? Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 30 & 48 & 66 & 84 \end{array}$ A tank starts with 14 gallons of water and fills at 12 gallons per minute. In $y = 12 x + 14$ , what does 12 mean? Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Linear Functions in Context

Date Period

Answer each question.

Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 23 & 43 & 63 & 83 \end{array}$
A plumber charges $90 for a visit plus $75 per hour. Write an equation for the total cost, $y$ , after $x$ hours.
A plant is 40 centimeters tall and grows 5 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks.
A plant is 59 centimeters tall and grows 2 centimeters a week. In $y = 2 x + 59$ , what does 2 mean?
A gym charges $20 to join and $35 per month. In $y = 35 x + 20$ , what does 35 mean?
A tank starts with 52 gallons of water and fills at 6 gallons per minute. In $y = 6 x + 52$ , what does 6 mean?
A tank starts with 26 gallons of water and fills at 12 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes.
A plumber charges $85 for a visit plus $105 per hour. In $y = 105 x + 85$ , what does 105 mean?
A gym charges $30 to join and $55 per month. Write an equation for the total paid, $y$ , after $x$ months.
Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 1 & 2 & 3 \\ y & 17 & 20 & 23 & 26 \end{array}$
A gym charges $25 to join and $25 per month. Write an equation for the total paid, $y$ , after $x$ months.
A tank starts with 27 gallons of water and fills at 3 gallons per minute. In $y = 3 x + 27$ , what does 3 mean?
A plumber charges $100 for a visit plus $85 per hour. In $y = 85 x + 100$ , what does 85 mean?
A gym charges $30 to join and $45 per month. In $y = 45 x + 30$ , what does 45 mean?
A plumber charges $100 for a visit plus $70 per hour. Write an equation for the total cost, $y$ , after $x$ hours.
A plant is 23 centimeters tall and grows 2 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks.
A tank starts with 10 gallons of water and fills at 3 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes.
A plant is 50 centimeters tall and grows 9 centimeters a week. In $y = 9 x + 50$ , what does 9 mean?
Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 30 & 48 & 66 & 84 \end{array}$
A tank starts with 14 gallons of water and fills at 12 gallons per minute. In $y = 12 x + 14$ , what does 12 mean?



Sigma Prep · sigmaprep.io/worksheets Name Linear Functions in ContextAnswer keyVersion 2 Date Period Answer each question. Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 23 & 43 & 63 & 83 \end{array}$ rate $10$ , initial value $23$ A plumber charges $90 for a visit plus $75 per hour. Write an equation for the total cost, $y$ , after $x$ hours. $y = 75 x + 90$ A plant is 40 centimeters tall and grows 5 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 5 x + 40$ A plant is 59 centimeters tall and grows 2 centimeters a week. In $y = 2 x + 59$ , what does 2 mean?For each extra week, its height goes up by 2 centimeters A gym charges $20 to join and $35 per month. In $y = 35 x + 20$ , what does 35 mean?For each extra month, the total paid goes up by $35 A tank starts with 52 gallons of water and fills at 6 gallons per minute. In $y = 6 x + 52$ , what does 6 mean?For each extra minute, the amount of water in the tank goes up by 6 gallons A tank starts with 26 gallons of water and fills at 12 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. $y = 12 x + 26$ A plumber charges $85 for a visit plus $105 per hour. In $y = 105 x + 85$ , what does 105 mean?For each extra hour, the total cost goes up by $105 A gym charges $30 to join and $55 per month. Write an equation for the total paid, $y$ , after $x$ months. $y = 55 x + 30$ Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 1 & 2 & 3 \\ y & 17 & 20 & 23 & 26 \end{array}$ rate $3$ , initial value $17$ A gym charges $25 to join and $25 per month. Write an equation for the total paid, $y$ , after $x$ months. $y = 25 x + 25$ A tank starts with 27 gallons of water and fills at 3 gallons per minute. In $y = 3 x + 27$ , what does 3 mean?For each extra minute, the amount of water in the tank goes up by 3 gallons A plumber charges $100 for a visit plus $85 per hour. In $y = 85 x + 100$ , what does 85 mean?For each extra hour, the total cost goes up by $85 A gym charges $30 to join and $45 per month. In $y = 45 x + 30$ , what does 45 mean?For each extra month, the total paid goes up by $45 A plumber charges $100 for a visit plus $70 per hour. Write an equation for the total cost, $y$ , after $x$ hours. $y = 70 x + 100$ A plant is 23 centimeters tall and grows 2 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 2 x + 23$ A tank starts with 10 gallons of water and fills at 3 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. $y = 3 x + 10$ A plant is 50 centimeters tall and grows 9 centimeters a week. In $y = 9 x + 50$ , what does 9 mean?For each extra week, its height goes up by 9 centimeters Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 30 & 48 & 66 & 84 \end{array}$ rate $9$ , initial value $30$ A tank starts with 14 gallons of water and fills at 12 gallons per minute. In $y = 12 x + 14$ , what does 12 mean?For each extra minute, the amount of water in the tank goes up by 12 gallons Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Linear Functions in ContextAnswer keyVersion 2

Date Period

Answer each question.

Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 23 & 43 & 63 & 83 \end{array}$ rate $10$ , initial value $23$
A plumber charges $90 for a visit plus $75 per hour. Write an equation for the total cost, $y$ , after $x$ hours. $y = 75 x + 90$
A plant is 40 centimeters tall and grows 5 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 5 x + 40$
A plant is 59 centimeters tall and grows 2 centimeters a week. In $y = 2 x + 59$ , what does 2 mean?For each extra week, its height goes up by 2 centimeters
A gym charges $20 to join and $35 per month. In $y = 35 x + 20$ , what does 35 mean?For each extra month, the total paid goes up by $35
A tank starts with 52 gallons of water and fills at 6 gallons per minute. In $y = 6 x + 52$ , what does 6 mean?For each extra minute, the amount of water in the tank goes up by 6 gallons
A tank starts with 26 gallons of water and fills at 12 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. $y = 12 x + 26$
A plumber charges $85 for a visit plus $105 per hour. In $y = 105 x + 85$ , what does 105 mean?For each extra hour, the total cost goes up by $105
A gym charges $30 to join and $55 per month. Write an equation for the total paid, $y$ , after $x$ months. $y = 55 x + 30$
Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 1 & 2 & 3 \\ y & 17 & 20 & 23 & 26 \end{array}$ rate $3$ , initial value $17$
A gym charges $25 to join and $25 per month. Write an equation for the total paid, $y$ , after $x$ months. $y = 25 x + 25$
A tank starts with 27 gallons of water and fills at 3 gallons per minute. In $y = 3 x + 27$ , what does 3 mean?For each extra minute, the amount of water in the tank goes up by 3 gallons
A plumber charges $100 for a visit plus $85 per hour. In $y = 85 x + 100$ , what does 85 mean?For each extra hour, the total cost goes up by $85
A gym charges $30 to join and $45 per month. In $y = 45 x + 30$ , what does 45 mean?For each extra month, the total paid goes up by $45
A plumber charges $100 for a visit plus $70 per hour. Write an equation for the total cost, $y$ , after $x$ hours. $y = 70 x + 100$
A plant is 23 centimeters tall and grows 2 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 2 x + 23$
A tank starts with 10 gallons of water and fills at 3 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. $y = 3 x + 10$
A plant is 50 centimeters tall and grows 9 centimeters a week. In $y = 9 x + 50$ , what does 9 mean?For each extra week, its height goes up by 9 centimeters
Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 30 & 48 & 66 & 84 \end{array}$ rate $9$ , initial value $30$
A tank starts with 14 gallons of water and fills at 12 gallons per minute. In $y = 12 x + 14$ , what does 12 mean?For each extra minute, the amount of water in the tank goes up by 12 gallons

How to do these

Find the rate of change and the initial value. $\begin{array}{cccc} x & 1 & 3 & 5 \\ y & 26 & 38 & 50 \end{array}$

From x = 1 to x = 3, y rises 12 while x rises 2, so the rate is 12 ÷ 2 = 6.
Work back one step from x = 1 to x = 0: 26 - 6 = 20.

The answer is rate $6$ , initial value $20$ .

Where students go wrong

Swapping the rate and the initial value. A gym that charges $20 to join and $35 a month is y = 35x + 20, not y = 20x + 35. The amount added each month is the one multiplied by x, and the one-time amount stands alone.

Also called linear models, rate of change and initial value or interpreting slope.

What you can put on this worksheet

Rate of change and initial value in context: Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 36 & 50 & 64 & 78 \end{array}$ → rate $7$ , initial value $36$
Use a model backwards: in what year: If $y$ is the height of a plant in centimeters and $x$ is weeks since it was planted, the model is $y = 4 x + 16$ . After how many weeks is it 24 cm tall? → $2$

Questions about these worksheets

Yes. Every linear functions in context 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 linear functions in context 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 2: rate of change and initial value in context and use a model backwards: in what year. Tick as many as you want and set how many of each, or let it spread them evenly.

Swapping the two numbers. The one charged every hour multiplies x; the one charged once is added on.

Linear functions in context worksheet for Pre-Algebra

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