1. What is Point Slope Form?

The point-slope form is a way to express the equation of a straight line using a known point on the line and the slope. It's particularly useful when you have two points and want to find the equation of the line passing through them.

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 plugs one point and the slope into the point-slope form equation.

3. Applications of Point Slope Form

Details: Point-slope form is widely used in algebra, geometry, physics, and engineering to describe linear relationships. It's particularly useful when you know specific points a line must pass through.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The points must have different x-coordinates to calculate a valid slope. Results are rounded to 4 decimal places for clarity.

5. Frequently Asked Questions (FAQ)

Q1: What if my 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 form to find y-intercept?
A: Yes, by setting x = 0 and solving for y, you can find the y-intercept from the point-slope form.

Q3: How is point-slope form different from 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.

Q4: What if my points have the same y-coordinate?
A: If y₁ = y₂, the line is horizontal with slope 0, and the equation becomes y = y₁.

Q5: Can I convert point-slope form to standard form?
A: Yes, by rearranging the terms: Ax + By = C, where A, B, and C are integers.