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 is positive, and A, B, and C have no common factors other than 1. This form is particularly useful for finding both x and y intercepts.

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 convert to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

3. Importance of Standard Form

Details: Standard form is useful for:

• Finding intercepts quickly (x-intercept = C/A, y-intercept = C/B)
• Describing vertical lines (when B = 0)
• Solving systems of equations
• Representing linear equations in a consistent format

4. Using the Calculator

Tips: Enter coefficients A, B, and constant C. The calculator will convert to slope-intercept form. For vertical lines (B=0), it will show the equation of the vertical line.

5. Frequently Asked Questions (FAQ)

Q1: Why convert to slope-intercept form?
A: Slope-intercept form makes it easy to identify the slope and y-intercept, which are useful for graphing and understanding the line's behavior.

Q2: What if B is zero?
A: When B=0, the equation represents a vertical line (x = constant), which has an undefined slope.

Q3: Can A or B be fractions?
A: While standard form typically uses integers, the calculator works with any real numbers.

Q4: How do I find intercepts from standard form?
A: x-intercept = C/A (set y=0), y-intercept = C/B (set x=0).

Q5: What's the advantage of standard form over slope-intercept?
A: Standard form can represent vertical lines and makes finding intercepts easier, while slope-intercept form is better for graphing.