1. What is Standard Form Linear Equation?

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for finding both x and y intercepts quickly and for solving systems of equations.

2. How Does the Calculator Work?

The calculator uses the standard form equation:

Where:

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

Solutions:

• x-intercept occurs when y=0: \( x = C/A \)
• y-intercept occurs when x=0: \( y = C/B \)

3. Importance of Standard Form

Details: The standard form makes it easy to find intercepts and is preferred when working with systems of linear equations. It's also useful for graphing as it directly shows both intercepts.

4. Using the Calculator

Tips: Enter coefficients A, B, and constant C. The calculator will display the equation in standard form and calculate both intercepts. Note that if A=0, the line is horizontal, and if B=0, the line is vertical.

5. Frequently Asked Questions (FAQ)

Q1: What if A or B is zero?
A: If A=0, the equation becomes By=C (horizontal line). If B=0, it becomes Ax=C (vertical line). The corresponding intercept will be undefined.

Q2: Can A, B, or C be fractions?
A: Yes, but standard form typically uses integers. The calculator accepts any real numbers.

Q3: How do I convert to slope-intercept form?
A: Solve for y: y = (-A/B)x + (C/B). The slope is -A/B and y-intercept is C/B.

Q4: What's the advantage over slope-intercept form?
A: Standard form can represent vertical lines (x = constant) which slope-intercept form cannot.

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