1. What is Slope-Intercept Form?

The slope-intercept form is a way to express the equation of a straight line. It is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept (the point where the line crosses the y-axis).

2. How Does the Calculator Work?

The calculator uses the slope-intercept formula:

Where:

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

Calculation Process: Given the slope (m) and a point (x, y) on the line, the calculator determines the y-intercept (b) using the formula: b = y - mx.

3. Importance of Slope-Intercept Form

Details: The slope-intercept form is fundamental in algebra and coordinate geometry. It provides a straightforward way to graph linear equations and understand the relationship between variables in various applications including physics, economics, and engineering.

4. Using the Calculator

Tips: Enter the known slope value, and the x and y coordinates of a point that lies on the line. The calculator will determine the y-intercept and display the complete equation in slope-intercept form.

5. Frequently Asked Questions (FAQ)

Q1: What if I have two points instead of a slope?
A: First calculate the slope using m = (y₂ - y₁)/(x₂ - x₁), then use one point to find the y-intercept.

Q2: Can this calculator handle negative values?
A: Yes, the calculator properly handles negative slopes and coordinates.

Q3: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line where y remains constant regardless of x.

Q4: How precise are the calculations?
A: Calculations are performed with high precision and results are rounded to 4 decimal places.

Q5: Can I use this for non-linear equations?
A: No, this calculator is specifically designed for linear equations in slope-intercept form.