1. What is the Point-Slope Form?

The point-slope form is a linear equation of a straight line that uses the slope of the line and the coordinates of a point on the line. It is particularly useful when you know one point on the line and its slope.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

Where:

• \( m \) — Slope of the line
• \( (x_1, y_1) \) — Coordinates of a known point on the line
• \( (x, y) \) — Coordinates of any other point on the line

Explanation: The formula expresses the relationship between the slope and the coordinates of points on the line.

3. Importance of Point-Slope Form

Details: The point-slope form is essential in algebra and coordinate geometry for quickly writing the equation of a line when a point and slope are known. It's particularly useful in calculus and physics applications.

4. Using the Calculator

Tips: Enter the slope (m) of the line and the coordinates (x₁, y₁) of a known point on the line. The calculator will provide both the point-slope form and slope-intercept form of the equation.

5. Frequently Asked Questions (FAQ)

Q1: How is point-slope form different from slope-intercept form?
A: Point-slope form uses a known point and slope, while slope-intercept form (y = mx + b) uses the slope and y-intercept.

Q2: Can I use any point on the line?
A: Yes, any known point on the line will work in the point-slope formula.

Q3: What if my slope is zero?
A: A zero slope means you have a horizontal line (y = constant).

Q4: What if my slope is undefined?
A: An undefined slope means you have a vertical line (x = constant).

Q5: How do I convert to standard form (Ax + By = C)?
A: Rearrange the equation by moving all terms to one side and eliminating fractions.