Equation converter
Choose a conversion direction and enter the equation values. The calculator accepts integers, decimals, and fractions. Clear validation messages explain unsupported or incomplete entries.
Formula used
Standard form is written as Ax + By = C. Move every variable term to the left side. Then clear fractions and reduce the integer coefficients.
| Starting form | Operation | Result |
|---|---|---|
| y = mx + b | Subtract mx | −mx + y = b |
| y = −8x − 1 | Add 8x | 8x + y = −1 |
| Ax + By = C | Solve for y | y = (−A/B)x + C/B |
How to use
- Select the required conversion direction.
- Enter a complete equation or separate coefficients.
- Choose fractions, decimals, or both result styles.
- Set the graph range and decimal precision.
- Press Calculate to view forms, steps, and intercepts.
- Copy, print, or export the completed calculation.
Example data
| Original equation | Standard form | General form |
|---|---|---|
| y = −8x − 1 | 8x + y = −1 | 8x + y + 1 = 0 |
| y = 3x + 4 | 3x − y = −4 | 3x − y + 4 = 0 |
| y = 1/2x − 2 | x − 2y = 4 | x − 2y − 4 = 0 |
| y = −x + 5 | x + y = 5 | x + y − 5 = 0 |
Frequently asked questions
What is standard form?
Standard form is Ax + By = C. A, B, and C are usually integers. Many classes also require A to remain positive.
What is the answer for y = −8x − 1?
Add 8x to both sides first. This gives 8x + y = −1. The coefficients are A = 8, B = 1, and C = −1.
Can the calculator use fractions?
Yes, fractions such as 1/2 are accepted. Their denominators are cleared automatically. The final standard form uses simplified integer coefficients.
Can it convert standard form backward?
Yes, choose the reverse conversion direction. Enter A, B, and C separately. The calculator solves the equation for y.
Why should A be positive?
A positive A creates a consistent conventional form. Multiplying every term by negative one preserves equality. The represented line does not change.
What happens when B equals zero?
The equation represents a vertical line. A vertical line has undefined slope. It cannot be written as y = mx + b.
How are decimals simplified?
Decimals are converted into exact fractions first. A common denominator clears every fractional coefficient. The result is reduced by the greatest common factor.
How are intercepts calculated?
Set y to zero for the x-intercept. Set x to zero for the y-intercept. The calculator reports both whenever they exist.
Does rearranging change the line?
No, valid operations create equivalent equations. Every point satisfying one form satisfies the other. The graph therefore remains exactly the same.