1. What is the Point-Slope Formula?

The point-slope form is a way to express the equation of a straight line when you know one point on the line and its slope. The formula is expressed as y - y₁ = m(x - x₁), where (x₁, y₁) is a known point and m is the slope of the line.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

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 calculator also verifies if a second point lies on the line defined by the first point and slope.

3. Importance of Line Equations

Details: Line equations are fundamental in mathematics and have applications across various fields including physics, engineering, economics, and computer graphics. They help model linear relationships between variables.

4. Using the Calculator

Tips: Enter the coordinates of one point (x₁, y₁), the slope (m), and the coordinates of a second point (x₂, y₂) to verify if it lies on the line. All values should be numerical.

5. Frequently Asked Questions (FAQ)

Q1: What if my slope is zero?
A: A slope of zero indicates a horizontal line. The equation would be y = y₁ (a constant value).

Q2: What if my slope is undefined?
A: An undefined slope indicates a vertical line. The equation would be x = x₁ (a constant value).

Q3: Can I convert point-slope form to slope-intercept form?
A: Yes, by solving for y: y = m(x - x₁) + y₁, which simplifies to y = mx + (y₁ - mx₁).

Q4: What's the difference between point-slope and slope-intercept form?
A: Point-slope uses a specific point and slope, while slope-intercept (y = mx + b) uses the slope and y-intercept.

Q5: How accurate is the point verification?
A: The verification allows for a small margin of error (0.001) to account for potential rounding in calculations.