1. What is the Point-Slope Form Equation?

The point-slope form equation \( y - y₁ = m(x - x₁) \) is a linear equation that defines a line using its slope and a single point on the line. It's particularly useful when you know one point and the slope of 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 known point (unitless)
• \( m \) — Slope of the line (unitless)
• \( x \) — Independent variable (unitless)
• \( x₁ \) — X-coordinate of known point (unitless)

Explanation: The equation calculates the relationship between x and y coordinates using a known point and the slope of 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 given a point and slope. It's particularly useful in graphing and solving linear equations.

4. Using the Calculator

Tips: Enter the y-coordinate of the point, the slope value, and the x-coordinate of the point. All values are unitless as this is a mathematical equation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between point-slope and 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.

Q2: Can I use this for vertical lines?
A: No, vertical lines have undefined slope and require a different approach (x = constant).

Q3: How do I convert to slope-intercept form?
A: Distribute the slope and solve for y: y = mx - mx₁ + y₁.

Q4: What if I have two points instead of slope and one point?
A: Calculate the slope first using (y₂ - y₁)/(x₂ - x₁), then use either point with the point-slope form.

Q5: Are there real-world applications of this equation?
A: Yes, it's used in physics for motion equations, economics for trend lines, and engineering for linear relationships.