Worksheets · Algebra 1

Linear functions in context worksheet

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.

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Name

Linear Functions in Context

Date Period

Answer each question.

  1. A tank starts with 5 gallons of water and fills at 8 gallons per minute. In y=8x+5, what does 8 mean?
  2. A tank starts with 45 gallons of water and fills at 8 gallons per minute. In y=8x+45, what does 8 mean?
  3. A plumber charges a $27 visit fee plus $3 per hour. Write an equation for the total cost, y, after x hours.
  4. A tank starts with 47 gallons of water and fills at 6 gallons per minute. Write an equation for the amount of water in the tank, y, after x minutes.
  5. A gym charges $49 to join and $8 per month. Write an equation for the total paid, y, after x months.
  6. Find the rate of change and the initial value.x0246y15355575
  7. A plumber charges a $47 visit fee plus $4 per hour. Write an equation for the total cost, y, after x hours.
  8. A plumber charges a $45 visit fee plus $3 per hour. Write an equation for the total cost, y, after x hours.
  9. A tank starts with 53 gallons of water and fills at 8 gallons per minute. In y=8x+53, what does 8 mean?
  10. A plant is 42 centimeters tall and grows 5 centimeters a week. In y=5x+42, what does 5 mean?
  11. A tank starts with 57 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.
  12. A gym charges $33 to join and $11 per month. In y=11x+33, what does 11 mean?
  13. A plumber charges a $12 visit fee plus $12 per hour. Write an equation for the total cost, y, after x hours.
  14. Find the rate of change and the initial value.x0123y23293541
  15. A plant is 52 centimeters tall and grows 10 centimeters a week. Write an equation for its height, y, after x weeks.
  16. Find the rate of change and the initial value.x0123y13182328
  17. A plumber charges a $8 visit fee plus $3 per hour. In y=3x+8, what does 3 mean?
  18. A plant is 34 centimeters tall and grows 7 centimeters a week. In y=7x+34, what does 7 mean?
  19. A plant is 53 centimeters tall and grows 12 centimeters a week. Write an equation for its height, y, after x weeks.
  20. A plant is 45 centimeters tall and grows 5 centimeters a week. Write an equation for its height, y, after x weeks.

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.

  1. A tank starts with 5 gallons of water and fills at 8 gallons per minute. In y=8x+5, what does 8 mean?For each extra minute, the amount of water in the tank goes up by 8
  2. 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
  3. A plumber charges a $27 visit fee plus $3 per hour. Write an equation for the total cost, y, after x hours.y=3x+27
  4. A tank starts with 47 gallons of water and fills at 6 gallons per minute. Write an equation for the amount of water in the tank, y, after x minutes.y=6x+47
  5. A gym charges $49 to join and $8 per month. Write an equation for the total paid, y, after x months.y=8x+49
  6. Find the rate of change and the initial value.x0246y15355575rate 10, initial value 15
  7. A plumber charges a $47 visit fee plus $4 per hour. Write an equation for the total cost, y, after x hours.y=4x+47
  8. A plumber charges a $45 visit fee plus $3 per hour. Write an equation for the total cost, y, after x hours.y=3x+45
  9. A tank starts with 53 gallons of water and fills at 8 gallons per minute. In y=8x+53, what does 8 mean?For each extra minute, the amount of water in the tank goes up by 8
  10. A plant is 42 centimeters tall and grows 5 centimeters a week. In y=5x+42, what does 5 mean?For each extra week, its height goes up by 5
  11. A tank starts with 57 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=11x+57
  12. A gym charges $33 to join and $11 per month. In y=11x+33, what does 11 mean?For each extra month, the total paid goes up by 11
  13. A plumber charges a $12 visit fee plus $12 per hour. Write an equation for the total cost, y, after x hours.y=12x+12
  14. Find the rate of change and the initial value.x0123y23293541rate 6, initial value 23
  15. A plant is 52 centimeters tall and grows 10 centimeters a week. Write an equation for its height, y, after x weeks.y=10x+52
  16. Find the rate of change and the initial value.x0123y13182328rate 5, initial value 13
  17. A plumber charges a $8 visit fee plus $3 per hour. In y=3x+8, what does 3 mean?For each extra hour, the total cost goes up by 3
  18. A plant is 34 centimeters tall and grows 7 centimeters a week. In y=7x+34, what does 7 mean?For each extra week, its height goes up by 7
  19. A plant is 53 centimeters tall and grows 12 centimeters a week. Write an equation for its height, y, after x weeks.y=12x+53
  20. A plant is 45 centimeters tall and grows 5 centimeters a week. Write an equation for its height, y, after x weeks.y=5x+45

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A plumber charges a $45 visit fee plus $30 per hour. Write the total cost after x hours.

  1. The fee is paid once: that is the starting value.
  2. Each hour adds 30: that is the rate.

The answer is y=30x+45.

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.

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.

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