1. What is the Slope from Standard Form?

The slope from standard form (Ax + By = C) is calculated as m = -A/B. This formula converts the standard form equation to slope-intercept form (y = mx + b) to determine the slope of the line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( A \) — Coefficient of x in standard form equation
• \( B \) — Coefficient of y in standard form equation

Explanation: The formula derives from rearranging the standard form equation to solve for y, revealing the slope as the coefficient of x in the resulting equation.

3. Importance of Slope Calculation

Details: The slope measures the steepness and direction of a line. It's essential in algebra, physics, engineering, and economics for understanding rates of change.

4. Using the Calculator

Tips: Enter the coefficients A and B from your standard form equation (Ax + By = C). B cannot be zero (vertical lines have undefined slope).

5. Frequently Asked Questions (FAQ)

Q1: What if B is zero?
A: When B=0, the line is vertical and the slope is undefined (infinite).

Q2: How does this relate to slope-intercept form?
A: The slope m in y = mx + b is exactly -A/B from standard form Ax + By = C.

Q3: What does a negative slope mean?
A: A negative slope means the line decreases as x increases (falls left to right).

Q4: Can I use this for any linear equation?
A: Yes, any linear equation can be converted to standard form to use this formula.

Q5: How precise are the results?
A: Results are precise to 4 decimal places, sufficient for most applications.