1. What is Point-Slope Form?

The point-slope form is a linear equation format that describes a line using its slope and a single point on the line. It is expressed as \( y - y_1 = m(x - x_1) \), 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 a point on the line
• \( y_1 \) — Y-coordinate of a point on the line
• \( x \) — Independent variable
• \( y \) — Dependent variable

Explanation: This form is particularly useful when you know one point on the line and the slope, making it easy to 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 quickly determining the equation of a line. It's particularly valuable in Desmos graphing and other mathematical applications where specific points and slopes are known.

4. Using the Calculator

Tips: Enter the slope value (m), and the coordinates of a point (x₁, y₁) on the line. The calculator will generate the complete point-slope form equation that can be used in Desmos or other graphing tools.

5. Frequently Asked Questions (FAQ)

Q1: How is point-slope form different from slope-intercept form?
A: Point-slope form uses a specific point and slope (\( y - y_1 = m(x - x_1) \)), while slope-intercept form uses slope and y-intercept (\( y = mx + b \)).

Q2: Can I use this form in Desmos graphing calculator?
A: Yes, Desmos accepts point-slope form equations directly. Simply enter the equation as calculated.

Q3: What if my slope is zero or undefined?
A: For zero slope (horizontal line), the equation becomes \( y = y_1 \). For undefined slope (vertical line), use \( x = x_1 \).

Q4: How do I convert point-slope form to slope-intercept form?
A: Distribute the slope and solve for y: \( y = m(x - x_1) + y_1 \).

Q5: Can I use decimal values for coordinates and slope?
A: Yes, the calculator accepts decimal values for all inputs, making it compatible with real-world data and precise calculations.