1. What is the Standard Form of a Linear Equation?

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers (usually), A should be positive, and A, B, and C should have no common factors other than 1. This form is particularly useful for finding both x and y intercepts easily.

2. How Does the Calculator Work?

The calculator converts standard form to slope-intercept form:

Where:

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

Explanation: The calculator solves for y to find the slope (m) and y-intercept (b) in the slope-intercept form y = mx + b.

3. Importance of Standard Form

Details: Standard form is useful for:

• Finding intercepts quickly (set x=0 for y-intercept, y=0 for x-intercept)
• Describing vertical lines (B=0)
• Working with systems of equations
• Graphing using intercepts

4. Using the Calculator

Tips: Enter integer values for A, B, and C. For best results:

• A should be positive
• A, B, and C should have no common factors
• B cannot be zero if you want to convert to slope-intercept form

5. Frequently Asked Questions (FAQ)

Q1: What if B is zero?
A: When B=0, the equation becomes Ax = C, which represents a vertical line. Slope is undefined in this case.

Q2: How do I find intercepts from standard form?
A: X-intercept: set y=0 and solve for x (x = C/A). Y-intercept: set x=0 and solve for y (y = C/B).

Q3: Can I use fractions or decimals?
A: While the calculator accepts decimals, standard form is typically written with integer coefficients.

Q4: How do I convert from slope-intercept to standard form?
A: Move all terms to one side: y = mx + b → mx - y = -b. Multiply to eliminate fractions if needed.

Q5: Why is standard form useful?
A: It's the preferred form for solving systems of equations and makes finding intercepts straightforward.