1. What is Standard Form in Algebra?

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 quickly identifying the x- and y-intercepts of the line.

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) of the line.

3. Importance of Standard Form

Details: Standard form is particularly useful for solving systems of equations and for representing vertical lines (when B=0) which cannot be represented in slope-intercept form.

4. Using the Calculator

Tips: Enter the coefficients A, B, and C from your standard form equation. The calculator will convert it to slope-intercept form or identify if it's a vertical line.

5. Frequently Asked Questions (FAQ)

Q1: What if B is zero?
A: When B=0, the equation represents a vertical line (x = constant) which cannot be expressed in slope-intercept form.

Q2: How do I find intercepts from standard form?
A: X-intercept is (C/A, 0), Y-intercept is (0, C/B) when A and B are non-zero.

Q3: Can A be negative in standard form?
A: While technically possible, conventionally A is kept non-negative by multiplying the entire equation by -1 if needed.

Q4: What's the advantage over slope-intercept form?
A: Standard form can represent all lines, including vertical ones, and is better for integer solutions.

Q5: How to convert to point-slope form?
A: First convert to slope-intercept form, then use any point on the line (like the y-intercept) to write in point-slope form.