1. What is the Standard Form Equation?

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers with no common factors (other than 1), and A is non-negative. It's useful for finding both x and y intercepts easily.

2. How Does the Calculator Work?

The calculator displays the equation in standard form:

Where:

• \( A \) — Coefficient of x (must be non-negative)
• \( B \) — Coefficient of y
• \( C \) — Constant term
• \( x \) — Independent variable
• \( y \) — Dependent variable

Explanation: The standard form is particularly useful for analyzing linear equations and finding intercepts quickly.

3. Importance of Standard Form

Details: The standard form makes it easy to find both x and y intercepts (set y=0 to find x-intercept, x=0 to find y-intercept). It's also the preferred form for many linear algebra operations.

4. Using the Calculator

Tips: Enter the coefficients A, B, and the constant C. The calculator will display the complete equation in standard form. All values can be positive or negative numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is A typically non-negative in standard form?
A: By convention, we prefer to write the equation with A ≥ 0 to maintain consistency, though mathematically negative values are equivalent.

Q2: How do I convert slope-intercept form to standard form?
A: Move all terms to one side of the equation (e.g., from y = mx + b to -mx + y = b), then adjust coefficients to be integers.

Q3: What if A, B, and C have common factors?
A: For true standard form, you should divide all terms by their greatest common divisor to simplify the equation.

Q4: Can B be zero in standard form?
A: Yes, if B=0 you get a vertical line (Ax = C). Similarly, if A=0 you get a horizontal line (By = C).

Q5: How do I find the slope from standard form?
A: The slope m = -A/B (when B ≠ 0). For B=0, the line is vertical with undefined slope.