Calculator
Enter values as integers, decimals, or fractions like 3/4.
Example Data Table
| Input Type | Given Values | Original Equation | Standard Form |
|---|---|---|---|
| Slope-intercept | m = 3/2, b = 4 | y = (3/2)x + 4 | 3x - 2y = -8 |
| Slope-intercept | m = -2, b = 5 | y = -2x + 5 | 2x + y = 5 |
| Point-slope | m = 1/3, (x₁, y₁) = (6, 4) | y - 4 = (1/3)(x - 6) | x - 3y = -6 |
| Two-point | (2, 5), (6, 11) | Through the two points | 3x - 2y = -4 |
Formula Used
1) From slope-intercept form
y = mx + b
Move the x-term to the left side, then clear denominators if needed. The standard form becomes Ax + By = C.
2) From point-slope form
y - y₁ = m(x - x₁)
Expand the right side, collect x and y terms, move constants, then simplify coefficients into integer form whenever possible.
3) From two points
A = y₂ - y₁, B = x₁ - x₂, C = x₁y₂ - x₂y₁
Ax + By = C
This direct coefficient method avoids separate slope calculation and works well for vertical, horizontal, and slanted lines.
Standardization rule
After forming the equation, multiply through by the least common multiple of denominators, divide by the greatest common divisor, and keep the leading coefficient nonnegative.
How to Use This Calculator
- Select the form that matches your equation data.
- Enter integers, decimals, or fractions into the relevant boxes.
- Press Convert to Standard Form.
- Read the simplified equation, coefficients, intercepts, and line type.
- Inspect the graph to confirm the line visually.
- Use the CSV or PDF buttons to save your result summary.
Frequently Asked Questions
1) What is standard form for a linear equation?
Standard form is usually written as Ax + By = C. A, B, and C are commonly integers, and many teachers prefer A to be nonnegative.
2) Can this calculator handle fractions?
Yes. You can enter values like 3/4, -5/2, 1.25, or whole numbers. The calculator converts them exactly before simplifying the final equation.
3) Why does the sign sometimes flip?
Multiplying both sides by -1 keeps the same line. The calculator flips signs when needed so the first nonzero coefficient is positive and cleaner to read.
4) Does it work for vertical lines?
Yes. Vertical lines have an undefined slope and a zero y-coefficient. A result like x = 4 is still valid standard form, written as 1x + 0y = 4.
5) What if my two points are the same?
A unique line cannot be formed from one repeated point. The calculator stops and shows an error so you can enter two distinct coordinates.
6) Why are denominators cleared?
Clearing denominators produces integer coefficients, which is the most common classroom and textbook expectation for standard form.
7) Can I use decimals instead of fractions?
Yes. Decimals are converted into exact rational values first, then simplified. This helps preserve accuracy before the final form is shown.
8) What do the graph and intercepts help me verify?
They confirm the equation describes the same line. The graph, slope, and intercepts make it easier to catch sign mistakes or incorrect rearrangement.