1. What is the Slope-Point Equation?

The slope-point equation is a fundamental linear equation form that defines a line using its slope and a specific point on the line. The equation is expressed as y - y₁ = m(x - x₁), where m represents the slope and (x₁, y₁) is a known point on the line.

2. How Does the Calculator Work?

The calculator uses the slope-point equation:

Where:

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

Explanation: The equation calculates the relationship between any point (x, y) on the line and the known point (x₁, y₁) using the slope m.

3. Importance of Slope-Point Form

Details: The slope-point form is particularly useful when you know one point on the line and the slope. It provides a straightforward way to write the equation of a line without needing the y-intercept.

4. Using the Calculator

Tips: Enter the slope value (m), and the coordinates of the known point (x₁, y₁). The calculator will provide both the slope-point form and slope-intercept form of the equation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between slope-point and slope-intercept form?
A: Slope-point form uses a specific point and slope (y - y₁ = m(x - x₁)), while slope-intercept form uses slope and y-intercept (y = mx + b).

Q2: Can I convert slope-point form to slope-intercept form?
A: Yes, by solving for y: y = m(x - x₁) + y₁, which simplifies to y = mx + (y₁ - mx₁).

Q3: When is slope-point form most useful?
A: When you know a point on the line and the slope, but not the y-intercept, or when working with tangent lines in calculus.

Q4: What does a zero slope mean in this equation?
A: A zero slope (m = 0) indicates a horizontal line where y remains constant regardless of x changes.

Q5: What about undefined slope?
A: An undefined slope indicates a vertical line, which cannot be represented in slope-point form and requires the equation x = x₁.