Worksheets · Algebra 1

Standard form of a linear equation worksheet

Standard form is Ax + By = C with whole-number coefficients, A positive, and nothing left to cancel. Easy converts from slope-intercept form, which means clearing the fraction and moving the x term across. Medium starts from a point and a slope, hard from two points. Every level also goes the other way, from standard form to slope-intercept form.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Standard Form of a Line

Date Period

Write each equation in the form asked for.

  1. Write in standard form

    Write the standard form of the line through (6,−7) with slope −52.
  2. Write the standard form of the line through (2,−6) with slope −4.
  3. Write the standard form of the line through (−6,22) with slope −73.
  4. Write the standard form of the line through (−9,−10) with slope 23.
  5. Write the standard form of the line through (1,16) with slope 9.
  6. Write the standard form of the line through (−6,4) with slope 23.
  7. Write the standard form of the line through (−1,7) with slope −6.
  8. Write the standard form of the line through (0,1) with slope −92.
  9. Write the standard form of the line through (3,−5) with slope 13.
  10. Write the standard form of the line through (−2,−18) with slope 6.

  1. Rewrite standard form as slope-intercept

    Write in slope-intercept form: 6x−6y=−2
  2. Write in slope-intercept form: −6x+5y=−15
  3. Write in slope-intercept form: −3x−2y=−17
  4. Write in slope-intercept form: 2x+5y=−5
  5. Write in slope-intercept form: 8x−y=18
  6. Write in slope-intercept form: −4x−4y=0
  7. Write in slope-intercept form: −x−5y=7
  8. Write in slope-intercept form: −x+y=10
  9. Write in slope-intercept form: −6x+y=−21
  10. Write in slope-intercept form: 8x−4y=19

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

Sigma Prep · sigmaprep.io/worksheets

Name

Standard Form of a LineAnswer keyVersion 1

Date Period

Write each equation in the form asked for.

  1. Write in standard form

    Write the standard form of the line through (6,−7) with slope −52.5x+2y=16
  2. Write the standard form of the line through (2,−6) with slope −4.4x+y=2
  3. Write the standard form of the line through (−6,22) with slope −73.7x+3y=24
  4. Write the standard form of the line through (−9,−10) with slope 23.2x−3y=12
  5. Write the standard form of the line through (1,16) with slope 9.9x−y=−7
  6. Write the standard form of the line through (−6,4) with slope 23.2x−3y=−24
  7. Write the standard form of the line through (−1,7) with slope −6.6x+y=1
  8. Write the standard form of the line through (0,1) with slope −92.9x+2y=2
  9. Write the standard form of the line through (3,−5) with slope 13.x−3y=18
  10. Write the standard form of the line through (−2,−18) with slope 6.6x−y=6

  1. Rewrite standard form as slope-intercept

    Write in slope-intercept form: 6x−6y=−2y=x+13
  2. Write in slope-intercept form: −6x+5y=−15y=65x−3
  3. Write in slope-intercept form: −3x−2y=−17y=−32x+172
  4. Write in slope-intercept form: 2x+5y=−5y=−25x−1
  5. Write in slope-intercept form: 8x−y=18y=8x−18
  6. Write in slope-intercept form: −4x−4y=0y=−x
  7. Write in slope-intercept form: −x−5y=7y=−15x−75
  8. Write in slope-intercept form: −x+y=10y=x+10
  9. Write in slope-intercept form: −6x+y=−21y=6x−21
  10. Write in slope-intercept form: 8x−4y=19y=2x−194

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

How to do these

Write y=23x−1 in standard form

  1. Multiply everything by 3: 3y = 2x - 3.
  2. Move the x term across: -2x + 3y = -3.
  3. A has to be positive, so multiply through by -1.

The answer is 2x−3y=3.

Where students go wrong

Leaving A negative, or leaving a fraction in. Both describe the same line, but neither is standard form, and neither will match a key.

Also called standard form, Ax + By = C or converting slope-intercept to standard form.

What you can put on this worksheet

Standard form
Write in standard form: y=4x+4 → 4x−y=−4
Standard form to slope-intercept form
Write in slope-intercept form: 5x+y=−1 → y=−5x−1
Fraction slope, from point-slope form
Write in standard form: y−2=7(x+4) → 7x−y=−30

Questions about these worksheets

Yes. Every standard form of a linear equation 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 standard form of a linear equation 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 3: standard form, standard form to slope-intercept form and fraction slope, from point-slope form. Tick as many as you want and set how many of each, or let it spread them evenly.

Leaving A negative, or leaving a fraction in. Both describe the same line, but neither is standard form, and neither will match a key.