1. What is Standard Form Equation?

The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero. This form is particularly useful for graphing and analyzing linear relationships.

2. How Does the Calculator Work?

The calculator uses the standard form equation:

Where:

• \( A \) — Coefficient of x
• \( B \) — Coefficient of y
• \( C \) — Constant term
• \( x \) — Independent variable
• \( y \) — Dependent variable

Explanation: The calculator finds intercepts and slope to help graph the equation. When A=0, the line is horizontal. When B=0, the line is vertical.

3. Graphing Standard Form Equations

Details: To graph the equation, you can find the x-intercept (set y=0) and y-intercept (set x=0), plot these points, and draw the line through them.

4. Using the Calculator

Tips: Enter coefficients A, B, and constant C. The calculator will provide intercepts and slope to help you graph the equation.

5. Frequently Asked Questions (FAQ)

Q1: What if both A and B are zero?
A: If A=B=0, you have either 0=C (no solution if C≠0, infinite solutions if C=0). Our calculator requires at least one non-zero coefficient.

Q2: 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.

Q3: What's special about standard form?
A: It clearly shows intercepts (x-intercept = C/A, y-intercept = C/B) and can represent vertical lines (B=0) which slope-intercept form cannot.

Q4: Can I use fractions or decimals?
A: Yes, the calculator accepts decimal inputs. For exact fractions, you may need to convert to decimals.

Q5: How do I graph vertical or horizontal lines?
A: For vertical lines (B=0), x = C/A. For horizontal lines (A=0), y = C/B.