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's 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 formula:

Where:

• \( y \) — Dependent variable (unitless)
• \( y₁ \) — y-coordinate of first point (unitless)
• \( m \) — Slope of the line (unitless)
• \( x \) — Independent variable (unitless)
• \( x₁ \) — x-coordinate of first point (unitless)
• \( y₂ \) — y-coordinate of second point (unitless)
• \( x₂ \) — x-coordinate of second point (unitless)

Explanation: The calculator first calculates the slope using two given points, then constructs the point-slope form equation using one of the points and the calculated slope.

3. Importance Of Point-Slope Form

Details: The point-slope form is particularly useful when you know one point on a line and its 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 coordinates of two distinct points. The calculator will compute the slope and generate the point-slope form equation. Note that if x₁ = x₂, the slope is undefined (vertical line).

5. Frequently Asked Questions (FAQ)

Q1: What if my points create a vertical line?
A: If x₁ = x₂, the slope is undefined and the equation is x = x₁ (a vertical line).

Q2: Can I use this form for horizontal lines?
A: Yes, for horizontal lines the slope is 0, and the equation becomes y = y₁.

Q3: How accurate is the calculation?
A: The calculation is mathematically exact, though results are displayed with 4 decimal places for readability.

Q4: 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.

Q5: Can I convert point-slope form to other linear equation forms?
A: Yes, point-slope form can be algebraically manipulated into slope-intercept form or standard form.