1. What is the Y-Intercept?

The y-intercept (b) is the point where a line crosses the y-axis of a graph. It represents the value of y when x equals zero in the linear equation y = mx + b.

2. How Does the Calculator Work?

The calculator uses the y-intercept formula:

Where:

• \( b \) — Y-intercept (value when x=0)
• \( y \) — Y-coordinate of a known point
• \( m \) — Slope of the line
• \( x \) — X-coordinate of a known point

Explanation: The formula rearranges the standard linear equation to solve for the y-intercept when you know one point on the line and the slope.

3. Importance of Y-Intercept

Details: The y-intercept is fundamental in linear equations and graphing. It provides a starting value in many real-world applications like physics, economics, and statistics.

4. Using the Calculator

Tips: Enter the y-value, slope (m), and x-value from any point on the line. The calculator will compute the y-intercept (b) where the line crosses the y-axis.

5. Frequently Asked Questions (FAQ)

Q1: What if my line is vertical?
A: Vertical lines have undefined slope and no y-intercept (they're parallel to the y-axis).

Q2: What if my line is horizontal?
A: Horizontal lines have slope (m) = 0, and the y-intercept equals the y-value at any point.

Q3: Can I find the y-intercept with two points?
A: Yes! First calculate the slope (m) between the two points, then use either point in the y-intercept formula.

Q4: What does a negative y-intercept mean?
A: It means the line crosses the y-axis below the origin (when x=0, y is negative).

Q5: How is this different from x-intercept?
A: The x-intercept is where y=0, while the y-intercept is where x=0.