1. What is the Line Equation from Slope and Point?

The point-slope form of a linear equation is used to find the equation of a line when you know the slope and one point on the line. This form is particularly useful in coordinate geometry and algebra.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

Where:

• \( y \) — Dependent variable (unitless)
• \( y_1 \) — Y-coordinate of known point (unitless)
• \( m \) — Slope of the line (unitless)
• \( x \) — Independent variable (unitless)
• \( x_1 \) — X-coordinate of known point (unitless)

Explanation: This formula directly relates the coordinates of any point (x, y) on the line to a known point (x₁, y₁) and the slope m.

3. Importance of Line Equations

Details: Line equations are fundamental in mathematics, physics, engineering, and data analysis. They help model linear relationships, predict values, and solve problems involving rates of change.

4. Using the Calculator

Tips: Enter the slope value, and the coordinates of the known point. The calculator will provide both the point-slope form and the slope-intercept form of the equation.

5. Frequently Asked Questions (FAQ)

Q1: What is 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 the equation x = constant.

Q3: What if my slope is zero?
A: A zero slope indicates a horizontal line with equation y = constant.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact when correct values are provided.

Q5: Can I use this for non-linear equations?
A: No, this formula is specifically for linear equations only.