A tank starts with 45 gallons of water and fills at 8 gallons per minute. In y = 8x + 45, what does 8 mean?

For each extra minute, the amount of water in the tank goes up by 8 gallons

A plumber charges $75 for a visit plus $95 per hour. In y = 95x + 75, what does 95 mean?

For each extra hour, the total cost goes up by $95

A plant is 56 centimeters tall and grows 7 centimeters a week. In y = 7x + 56, what does 7 mean?

For each extra week, its height goes up by 7 centimeters

A gym charges $50 to join and $20 per month. In y = 20x + 50, what does 20 mean?

For each extra month, the total paid goes up by $20

A plumber charges $40 for a visit plus $65 per hour. In y = 65x + 40, what does 65 mean?

For each extra hour, the total cost goes up by $65

A tank starts with 60 gallons of water and fills at 9 gallons per minute. In y = 9x + 60, what does 9 mean?

For each extra minute, the amount of water in the tank goes up by 9 gallons

A plant is 9 centimeters tall and grows 3 centimeters a week. In y = 3x + 9, what does 3 mean?

For each extra week, its height goes up by 3 centimeters

A gym charges $75 to join and $25 per month. In y = 25x + 75, what does 25 mean?

For each extra month, the total paid goes up by $25

A plumber charges $70 for a visit plus $110 per hour. In y = 110x + 70, what does 110 mean?

For each extra hour, the total cost goes up by $110

Worksheets · Algebra 1

Linear functions in context worksheet for Algebra 1

In y = mx + b the slope m is the rate of change, what y gains for each 1 of x, and b is the initial value, what y is when x is 0. A fee plus a charge per hour is exactly this shape.

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

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

Writing Linear Equations (Algebra 1). Slope-intercept, point-slope and standard form.
Graphing Linear Equations (Algebra 1). 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. A tank starts with 45 gallons of water and fills at 8 gallons per minute. In $y = 8 x + 45$ , what does 8 mean? Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 1 & 2 & 3 \\ y & 60 & 66 & 72 & 78 \end{array}$ A plant is 15 centimeters tall and grows 4 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. A plumber charges $75 for a visit plus $95 per hour. In $y = 95 x + 75$ , what does 95 mean? A plumber charges $85 for a visit plus $50 per hour. Write an equation for the total cost, $y$ , after $x$ hours. A plant is 56 centimeters tall and grows 7 centimeters a week. In $y = 7 x + 56$ , what does 7 mean? A tank starts with 33 gallons of water and fills at 11 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. A gym charges $25 to join and $35 per month. Write an equation for the total paid, $y$ , after $x$ months. A gym charges $50 to join and $20 per month. In $y = 20 x + 50$ , what does 20 mean? A plumber charges $40 for a visit plus $65 per hour. In $y = 65 x + 40$ , what does 65 mean? Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 30 & 44 & 58 & 72 \end{array}$ A tank starts with 60 gallons of water and fills at 9 gallons per minute. In $y = 9 x + 60$ , what does 9 mean? A gym charges $90 to join and $60 per month. Write an equation for the total paid, $y$ , after $x$ months. A plant is 9 centimeters tall and grows 3 centimeters a week. In $y = 3 x + 9$ , what does 3 mean? A plumber charges $90 for a visit plus $80 per hour. Write an equation for the total cost, $y$ , after $x$ hours. A gym charges $75 to join and $25 per month. In $y = 25 x + 75$ , what does 25 mean? A plant is 51 centimeters tall and grows 4 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. A tank starts with 7 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 47 centimeters tall and grows 3 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. A plumber charges $70 for a visit plus $110 per hour. In $y = 110 x + 70$ , what does 110 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.

A tank starts with 45 gallons of water and fills at 8 gallons per minute. In $y = 8 x + 45$ , what does 8 mean?
Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 1 & 2 & 3 \\ y & 60 & 66 & 72 & 78 \end{array}$
A plant is 15 centimeters tall and grows 4 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks.
A plumber charges $75 for a visit plus $95 per hour. In $y = 95 x + 75$ , what does 95 mean?
A plumber charges $85 for a visit plus $50 per hour. Write an equation for the total cost, $y$ , after $x$ hours.
A plant is 56 centimeters tall and grows 7 centimeters a week. In $y = 7 x + 56$ , what does 7 mean?
A tank starts with 33 gallons of water and fills at 11 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes.
A gym charges $25 to join and $35 per month. Write an equation for the total paid, $y$ , after $x$ months.
A gym charges $50 to join and $20 per month. In $y = 20 x + 50$ , what does 20 mean?
A plumber charges $40 for a visit plus $65 per hour. In $y = 65 x + 40$ , what does 65 mean?
Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 30 & 44 & 58 & 72 \end{array}$
A tank starts with 60 gallons of water and fills at 9 gallons per minute. In $y = 9 x + 60$ , what does 9 mean?
A gym charges $90 to join and $60 per month. Write an equation for the total paid, $y$ , after $x$ months.
A plant is 9 centimeters tall and grows 3 centimeters a week. In $y = 3 x + 9$ , what does 3 mean?
A plumber charges $90 for a visit plus $80 per hour. Write an equation for the total cost, $y$ , after $x$ hours.
A gym charges $75 to join and $25 per month. In $y = 25 x + 75$ , what does 25 mean?
A plant is 51 centimeters tall and grows 4 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks.
A tank starts with 7 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 47 centimeters tall and grows 3 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks.
A plumber charges $70 for a visit plus $110 per hour. In $y = 110 x + 70$ , what does 110 mean?



Sigma Prep · sigmaprep.io/worksheets Name Linear Functions in ContextAnswer keyVersion 1 Date Period Answer each question. A tank starts with 45 gallons of water and fills at 8 gallons per minute. In $y = 8 x + 45$ , what does 8 mean?For each extra minute, the amount of water in the tank goes up by 8 gallons Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 1 & 2 & 3 \\ y & 60 & 66 & 72 & 78 \end{array}$ rate $6$ , initial value $60$ A plant is 15 centimeters tall and grows 4 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 4 x + 15$ A plumber charges $75 for a visit plus $95 per hour. In $y = 95 x + 75$ , what does 95 mean?For each extra hour, the total cost goes up by $95 A plumber charges $85 for a visit plus $50 per hour. Write an equation for the total cost, $y$ , after $x$ hours. $y = 50 x + 85$ A plant is 56 centimeters tall and grows 7 centimeters a week. In $y = 7 x + 56$ , what does 7 mean?For each extra week, its height goes up by 7 centimeters A tank starts with 33 gallons of water and fills at 11 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. $y = 11 x + 33$ A gym charges $25 to join and $35 per month. Write an equation for the total paid, $y$ , after $x$ months. $y = 35 x + 25$ A gym charges $50 to join and $20 per month. In $y = 20 x + 50$ , what does 20 mean?For each extra month, the total paid goes up by $20 A plumber charges $40 for a visit plus $65 per hour. In $y = 65 x + 40$ , what does 65 mean?For each extra hour, the total cost goes up by $65 Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 30 & 44 & 58 & 72 \end{array}$ rate $7$ , initial value $30$ A tank starts with 60 gallons of water and fills at 9 gallons per minute. In $y = 9 x + 60$ , what does 9 mean?For each extra minute, the amount of water in the tank goes up by 9 gallons A gym charges $90 to join and $60 per month. Write an equation for the total paid, $y$ , after $x$ months. $y = 60 x + 90$ A plant is 9 centimeters tall and grows 3 centimeters a week. In $y = 3 x + 9$ , what does 3 mean?For each extra week, its height goes up by 3 centimeters A plumber charges $90 for a visit plus $80 per hour. Write an equation for the total cost, $y$ , after $x$ hours. $y = 80 x + 90$ A gym charges $75 to join and $25 per month. In $y = 25 x + 75$ , what does 25 mean?For each extra month, the total paid goes up by $25 A plant is 51 centimeters tall and grows 4 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 4 x + 51$ A tank starts with 7 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. $y = 3 x + 7$ A plant is 47 centimeters tall and grows 3 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 3 x + 47$ A plumber charges $70 for a visit plus $110 per hour. In $y = 110 x + 70$ , what does 110 mean?For each extra hour, the total cost goes up by $110 Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Linear Functions in ContextAnswer keyVersion 1

Date Period

Answer each question.

A tank starts with 45 gallons of water and fills at 8 gallons per minute. In $y = 8 x + 45$ , what does 8 mean?For each extra minute, the amount of water in the tank goes up by 8 gallons
Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 1 & 2 & 3 \\ y & 60 & 66 & 72 & 78 \end{array}$ rate $6$ , initial value $60$
A plant is 15 centimeters tall and grows 4 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 4 x + 15$
A plumber charges $75 for a visit plus $95 per hour. In $y = 95 x + 75$ , what does 95 mean?For each extra hour, the total cost goes up by $95
A plumber charges $85 for a visit plus $50 per hour. Write an equation for the total cost, $y$ , after $x$ hours. $y = 50 x + 85$
A plant is 56 centimeters tall and grows 7 centimeters a week. In $y = 7 x + 56$ , what does 7 mean?For each extra week, its height goes up by 7 centimeters
A tank starts with 33 gallons of water and fills at 11 gallons per minute. Write an equation for the amount of water in the tank, $y$ , after $x$ minutes. $y = 11 x + 33$
A gym charges $25 to join and $35 per month. Write an equation for the total paid, $y$ , after $x$ months. $y = 35 x + 25$
A gym charges $50 to join and $20 per month. In $y = 20 x + 50$ , what does 20 mean?For each extra month, the total paid goes up by $20
A plumber charges $40 for a visit plus $65 per hour. In $y = 65 x + 40$ , what does 65 mean?For each extra hour, the total cost goes up by $65
Find the rate of change and the initial value. $\begin{array}{ccccc} x & 0 & 2 & 4 & 6 \\ y & 30 & 44 & 58 & 72 \end{array}$ rate $7$ , initial value $30$
A tank starts with 60 gallons of water and fills at 9 gallons per minute. In $y = 9 x + 60$ , what does 9 mean?For each extra minute, the amount of water in the tank goes up by 9 gallons
A gym charges $90 to join and $60 per month. Write an equation for the total paid, $y$ , after $x$ months. $y = 60 x + 90$
A plant is 9 centimeters tall and grows 3 centimeters a week. In $y = 3 x + 9$ , what does 3 mean?For each extra week, its height goes up by 3 centimeters
A plumber charges $90 for a visit plus $80 per hour. Write an equation for the total cost, $y$ , after $x$ hours. $y = 80 x + 90$
A gym charges $75 to join and $25 per month. In $y = 25 x + 75$ , what does 25 mean?For each extra month, the total paid goes up by $25
A plant is 51 centimeters tall and grows 4 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 4 x + 51$
A tank starts with 7 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. $y = 3 x + 7$
A plant is 47 centimeters tall and grows 3 centimeters a week. Write an equation for its height, $y$ , after $x$ weeks. $y = 3 x + 47$
A plumber charges $70 for a visit plus $110 per hour. In $y = 110 x + 70$ , what does 110 mean?For each extra hour, the total cost goes up by $110

How to do these

A plumber charges $65 for a visit plus $80 per hour. Write the total cost after $x$ hours.

The visit charge is paid once: that is the starting value.
Each hour adds 80: that is the rate.

The answer is $y = 80 x + 65$ .

Where students go wrong

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

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.

Algebra 1 is usually taken around 8th or 9th 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 Algebra 1

Select your difficulty

How to do these

Where students go wrong

What you can put on this worksheet

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