Standard Form Calculator — Convert Linear Equation Forms (Free)

Use this free standard form calculator to convert a linear equation between forms. Start from slope-intercept (y = mx + b) or standard form (Ax + By = C) and the tool gives you the other form, the slope, the intercepts, and the algebra in between.

How to use the calculator

1. Choose which form you’re starting from.
2. Enter numbers only, not the entire equation. For y = −0.5x + 4, enter −0.5 for m and 4 for b. For 3x − 2y = 8, enter A = 3, B = −2, C = 8.
3. Read the converted equation, the slope, and the intercepts. Enter coefficients with at most six decimal places and absolute values up to 9,000,000,000. Repeating results are displayed to six decimal places; use exact fractions in your written work when required.

The two forms

Slope-intercept form, y = mx + b, shows the slope and y-intercept directly. Standard form, Ax + By = C with integer A, B, C, is handy for finding intercepts and for systems of equations. The calculator clears fractions to give a tidy standard form.

Example: convert a decimal slope

Start with y = −0.5x + 4. Add 0.5x to both sides: 0.5x + y = 4. Multiply every term by 2 to get x + 2y = 8. The equivalent standard form has slope −1/2 and y-intercept 4. Setting y = 0 gives x = 8; setting x = 0 gives y = 4.

Example: convert standard form back

For 3x − 2y = 8, subtract 3x: −2y = −3x + 8. Divide every term by −2: y = 1.5x − 4. Keep the negative sign on B when entering the coefficients.

Vertical lines, intercepts and common questions

How do you convert slope-intercept to standard form?

Move the x-term to the left and clear any fractions so the equation reads Ax + By = C with integer coefficients (negative values are allowed). y = 2x + 3 becomes 2x − y = −3.

How do you find the slope from standard form?

For Ax + By = C with B ≠ 0, the slope is m = −A/B and the y-intercept is C/B. If B = 0 and A ≠ 0, the line is vertical and its slope is undefined.

What about vertical and horizontal lines?

If B = 0 and A ≠ 0, the line is vertical: x = C/A. If A = 0 and B ≠ 0, it is horizontal: y = C/B. A and B cannot both be zero for a line. The x-axis (y = 0) and y-axis (x = 0) overlap an axis rather than meeting it at one unique intercept.

Read the full lesson: learn the method step by step.

Practice the method after checking an answer

Pick two points from the original equation and substitute them into the converted equation. Both forms should accept the same points. If they do not, compare the signs and check that you multiplied or divided every term.

Use the standard-form lesson for the rearrangement method, or review finding slope if −A/B is the confusing step. For a wider sequence of lessons, worksheets and study-book options, visit the Algebra 1 learning center.

Further reading: OpenStax: graphing linear equations and finding intercepts.