1. What is the Point-Slope Form Equation?

The point-slope form is a linear equation format that defines a line using a known point on the line and its slope. It's particularly useful when you have two points and need to find the equation of the line passing through them.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

Where:

• \( m = \frac{y₂ - y₁}{x₂ - x₁} \) — Slope of the line
• \( (x₁, y₁) \) — Coordinates of the first point
• \( (x₂, y₂) \) — Coordinates of the second point

Explanation: The calculator first calculates the slope using the two given points, then substitutes one point and the slope into the point-slope form equation.

3. Importance of Line Equations

Details: Line equations are fundamental in mathematics and have wide applications in physics, engineering, economics, and computer graphics. They help model linear relationships between variables and solve various real-world problems.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will compute the slope and generate the line equation in point-slope form. For vertical lines (when x₁ = x₂), a special equation is displayed.

5. Frequently Asked Questions (FAQ)

Q1: What if the two points have the same x-coordinate?
A: When x₁ = x₂, the line is vertical and the equation becomes x = x₁ (or x = x₂).

Q2: Can I use this for decimal coordinates?
A: Yes, the calculator handles decimal coordinates and provides results with appropriate precision.

Q3: How accurate is the slope calculation?
A: The calculator provides slope values with up to 4 decimal places for precision.

Q4: What's the difference between point-slope and slope-intercept form?
A: Point-slope form uses a specific point and slope, while slope-intercept form (y = mx + b) uses the slope and y-intercept.

Q5: Can I convert the result to other forms?
A: Yes, the point-slope form can be algebraically manipulated into slope-intercept or standard form as needed.