Calculator
Enter values for the standard form equation Ax + By = C. Fractions, decimals, mixed numbers, and negative coefficients are supported.
Formula Used
Standard form: Ax + By = C
Move the x term: By = -Ax + C
Divide by B: y = (-A/B)x + C/B
Slope: m = -A/B
Y intercept: b = C/B
When B equals zero, the equation is vertical. A vertical line cannot be written as y = mx + b because its slope is undefined.
How to Use This Calculator
- Type the value of A from Ax + By = C.
- Type the value of B. Use zero only to check a vertical line.
- Type the value of C. Fractions and decimals are accepted.
- Choose decimal precision, or enable exact fraction output.
- Press the convert button. The result appears above the form.
- Review the slope, intercept, and step check before graphing.
Converting Linear Equations With Confidence
Why Convert Standard Form
Standard form is useful because it keeps both variables on one side. Many textbooks write a line as Ax + By = C. This format is compact. It also works well for intercepts. Yet graphing often feels easier in slope intercept form. The form y = mx + b shows two facts at once. The number m tells the slope. The number b tells where the line crosses the y axis. This calculator moves from one form to the other with clear algebra steps.
The key operation is isolating y. First, subtract Ax from both sides. That gives By = -Ax + C. Next, divide every term by B. The result is y = (-A/B)x + C/B. This means the slope is -A divided by B. The y intercept is C divided by B. The tool also flags special cases. If B is zero, the line is vertical. A vertical line has no slope intercept form.
Understanding the Output
The main answer gives the converted equation. The slope value appears separately. The y intercept value appears with its point. A sample point can also be shown. This is helpful when drawing a graph. It gives another ordered pair besides the intercept. You can enter a custom x value. The calculator then substitutes it into the final equation. This makes checking simple.
Exact fraction mode is useful for homework. It keeps values like -2/3 or 7/5 unchanged. Decimal mode is useful for quick estimates. You can set precision from zero to ten digits. Both views come from the same algebra. Use the one your class, report, or worksheet requires.
Accuracy Tips for Linear Equations
Always keep signs attached to each coefficient. In the equation -4x + 2y = 8, A is -4. B is 2. C is 8. Do not move the negative sign away from A. A small sign error changes the slope. Also check that the equation is truly in Ax + By = C order. If the right side contains x or y, simplify first. Combine like terms before using the calculator.
Fractions can make the answer look complex. That does not mean it is wrong. A line with A = 5 and B = 6 has slope -5/6. This is a normal result. For graphing, start at the y intercept. Then use rise over run from the slope. A negative slope moves down as x increases. A positive slope moves up as x increases. This makes the converted form practical for study and teaching.
You can also use the result to compare two lines. Equal slopes mean parallel lines when intercepts differ. Slopes that multiply to -1 usually show perpendicular lines. Because the calculator gives m directly, these checks become faster. It is also useful for geometry and graph review. The step display helps you learn the method instead of only copying the expression. That makes every conversion easier to trust.
FAQs
What is slope intercept form?
Slope intercept form is y = mx + b. The letter m is the slope. The letter b is the y intercept. This form is helpful because it shows how the line rises or falls and where it crosses the y axis.
How do I convert Ax + By = C?
Subtract Ax from both sides. Then divide each term by B. The final form is y = (-A/B)x + C/B. The slope is -A/B. The y intercept is C/B.
What happens when B is zero?
When B is zero, the equation becomes Ax = C. This is a vertical line. It can be written as x = C/A, but it cannot be written as y = mx + b because the slope is undefined.
Can A be zero?
Yes. If A is zero and B is not zero, the equation becomes By = C. After division, the result is y = C/B. This is a horizontal line with slope zero.
Does the calculator accept fractions?
Yes. You can enter fractions such as 3/4 or -5/2. You can also enter mixed numbers like 2 1/3. Enable exact fraction output when you want the answer shown as a simplified fraction.
What is the slope in standard form?
For Ax + By = C, the slope is -A/B when B is not zero. This comes from isolating y. The x coefficient becomes negative, then it is divided by the y coefficient.
What is the y intercept?
The y intercept is C/B when B is not zero. It is the value of y when x equals zero. The intercept point is written as (0, C/B).
Can I use decimals?
Yes. Decimal coefficients are supported. You can choose how many digits appear in the answer. For exact algebra work, fractions are often cleaner than rounded decimal values.
Why is my answer negative?
A negative answer often comes from the sign of A or B. Since slope is -A/B, changing either coefficient can change the slope sign. Check that each sign was entered correctly.
How can I check the result?
Pick an x value and calculate y from the converted equation. Substitute both values back into Ax + By = C. If the left side equals C, the conversion is correct.
Is standard form the same as slope intercept form?
No. Standard form is Ax + By = C. Slope intercept form is y = mx + b. They can describe the same line, but they present different details more clearly.