1. What is the Point Slope Formula?

The point-slope formula is a linear equation form that describes a line using a known point on the line and the slope of the line. It is expressed as y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

Where:

• \( x₁, y₁ \) — Coordinates of the first point
• \( x₂, y₂ \) — Coordinates of the second point
• \( m \) — Slope of the line
• \( x, y \) — Variables representing any point on the line

Explanation: The calculator first calculates the slope using the two given points, then constructs the point-slope equation using the first point and the calculated slope.

3. Importance of Point Slope Form

Details: The point-slope form is particularly useful when you know a point on the line and the slope, making it easy to write the equation of the line without needing the y-intercept.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The points must not have the same x-coordinate (which would result in a vertical line with undefined slope).

5. Frequently Asked Questions (FAQ)

Q1: What if the two points have the same x-coordinate?
A: If x₁ = x₂, the line is vertical and the slope is undefined. The equation would be x = x₁.

Q2: Can I use this calculator for any two points?
A: Yes, as long as the points are distinct and not vertically aligned (unless you want to handle the special case of vertical lines).

Q3: How accurate is the calculation?
A: The calculation is mathematically exact, though the result is rounded to 4 decimal places for display purposes.

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 point-slope form to other forms?
A: Yes, point-slope form can be algebraically manipulated into slope-intercept form or standard form (Ax + By = C).