1. What is Slope-Intercept Form?

The slope-intercept form is a way to express linear inequalities in the form y < mx + b (or similar inequalities). It shows the relationship between the dependent variable y and independent variable x, where m represents the slope and b represents the y-intercept.

2. How Does the Calculator Work?

The calculator converts inequality to slope-intercept form:

Where:

• \( y \) — Dependent variable (unitless)
• \( m \) — Slope (unitless)
• \( x \) — Independent variable (unitless)
• \( b \) — Y-intercept (unitless)

Explanation: The calculator takes the slope, x-value, and intercept to determine the inequality relationship and presents it in standard slope-intercept form.

3. Importance of Slope-Intercept Form

Details: Slope-intercept form is crucial for graphing linear inequalities, understanding rate of change, and solving systems of inequalities in algebra and calculus.

4. Using the Calculator

Tips: Enter the slope (m), independent variable value (x), intercept (b), and select the appropriate inequality type. The calculator will provide the result in slope-intercept form.

5. Frequently Asked Questions (FAQ)

Q1: What types of inequalities can this calculator handle?
A: The calculator handles all four basic inequality types: less than, greater than, less than or equal to, and greater than or equal to.

Q2: Are the variables unitless?
A: Yes, in this general form, all variables (y, m, x, b) are considered unitless for mathematical consistency.

Q3: Can I use this for graphing inequalities?
A: Yes, the slope-intercept form is ideal for graphing as it clearly shows the slope and y-intercept of the boundary line.

Q4: What if my slope is zero?
A: A zero slope creates a horizontal line, and the inequality becomes y < b (or similar), representing all points above or below the horizontal line.

Q5: How accurate are the results?
A: The calculator provides results with 4 decimal places precision, ensuring mathematical accuracy for most practical applications.