1. What is Point Slope Form?

The point slope form is a linear equation format used to describe a line using its slope and a single point on the line. It is expressed as y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

2. How Does the Calculator Work?

The calculator uses the point slope form equation:

Where:

• \( m \) — Slope of the line
• \( x_1 \) — X-coordinate of the point
• \( y_1 \) — Y-coordinate of the point

Explanation: This form is particularly useful when you know the slope of a line and one point that lies on it, allowing you to quickly write the equation of the line.

3. Importance of Point Slope Form

Details: The point slope form is essential in algebra and coordinate geometry for writing linear equations, graphing lines, and solving problems involving linear relationships between variables.

4. Using the Calculator

Tips: Enter the slope value (m), and the coordinates of the point (x₁, y₁). The calculator will generate the complete point slope form equation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between point slope form and slope intercept form?
A: Point slope form uses a specific point and slope (y - y₁ = m(x - x₁)), while slope intercept form uses slope and y-intercept (y = mx + b).

Q2: 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 through simplification.

Q3: When is point slope form most useful?
A: It's particularly useful when you're given the slope and one point on the line, or when you need to find the equation of a line parallel or perpendicular to another line through a specific point.

Q4: What if my slope is zero or undefined?
A: For zero slope (horizontal line), the equation becomes y = y₁. For undefined slope (vertical line), the equation becomes x = x₁.

Q5: Can I use this form for non-linear equations?
A: No, point slope form is specifically designed for linear equations and cannot be used for quadratic, exponential, or other non-linear functions.