1. What is the 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 - 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:

• \( y \) — Dependent variable (unitless)
• \( y₁ \) — Y-coordinate of point (unitless)
• \( m \) — Slope of the line (unitless)
• \( x \) — Independent variable (unitless)
• \( x₁ \) — X-coordinate of point (unitless)

Explanation: The equation represents a straight line with slope m that passes through the point (x₁, y₁).

3. Importance of Point-Slope Form

Details: The point-slope form is particularly useful when you know one point on the line and the slope. It's commonly used in calculus, physics, and engineering applications where instantaneous rates of change are important.

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

Q2: Can I convert point-slope form to slope-intercept form?
A: Yes, by simplifying and solving for y: y = m(x - x₁) + y₁.

Q3: When is point-slope form most useful?
A: When you have a point and slope but don't know the y-intercept, or when working with linear approximations in calculus.

Q4: What if my slope is zero or undefined?
A: With zero slope, you get a horizontal line (y = y₁). With undefined slope, you get a vertical line (x = x₁).

Q5: Can I use this form for non-linear equations?
A: No, the point-slope form is specifically for linear equations. For non-linear equations, different forms are used.