1. What is Point-Slope Form?

The point-slope form is a linear equation format used to describe a line when you know the slope and one point on the line. It's expressed as y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

2. How Does the Calculator Work?

The calculator uses the point-slope form equation:

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: The equation shows how the difference in y-values relates to the difference in x-values through the slope.

3. Importance of Point-Slope Form

Details: Point-slope form is particularly useful when you have a point and the slope, making it easier to write the equation of a line without needing the y-intercept. It's commonly used in calculus and physics applications.

4. Using the Calculator

Tips: Enter the y-coordinate of your point, the slope of the line, and the x-coordinate of your point. The calculator will provide both point-slope and slope-intercept forms of the equation.

5. Frequently Asked Questions (FAQ)

Q1: When should I use point-slope form?
A: Use point-slope form when you know one point on the line and the slope, especially when the y-intercept is not readily available.

Q2: How do I convert point-slope form to slope-intercept form?
A: Distribute the slope, then isolate y by adding y₁ to both sides: y = m(x - x₁) + y₁.

Q3: Can I use point-slope form with fractional slopes?
A: Yes, point-slope form works with any real number slope, including fractions and decimals.

Q4: What if my point has negative coordinates?
A: Negative coordinates work perfectly in the formula. The equation will handle the signs correctly.

Q5: How is point-slope form different from standard form?
A: Point-slope form emphasizes a specific point and slope, while standard form (Ax + By = C) emphasizes integer coefficients.