1. What is Point-Slope Form?

The point-slope form is a linear equation of a straight line that uses the slope and coordinates of a single point on the line. It's particularly useful when you know one point on the line and its slope.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

Where:

• \( m \) — Slope of the line
• \( (x_1, y_1) \) — Coordinates of a known point on the line

Explanation: The equation represents how any point (x,y) on the line relates to the known point (x₁,y₁) through the slope m.

3. Importance of Point-Slope Form

Details: Point-slope form is essential in algebra and coordinate geometry for quickly writing the equation of a line when given a point and slope. It's also easily converted to slope-intercept form (y = mx + b).

4. Using the Calculator

Tips: Enter the slope (m) and coordinates of one point on the line (x₁, y₁). The calculator will generate the equation in point-slope form.

5. Frequently Asked Questions (FAQ)

Q1: How is point-slope form different from slope-intercept form?
A: Point-slope form uses a specific point and slope, while slope-intercept form uses the slope and y-intercept. Both can represent the same line.

Q2: Can I use any point on the line?
A: Yes, any point (x₁,y₁) that lies on the line will work in the equation, though the specific equation will look different for different points.

Q3: How do I convert to slope-intercept form?
A: Simply solve for y: y = m(x - x₁) + y₁ → y = mx - mx₁ + y₁.

Q4: What if my slope is zero or undefined?
A: For zero slope (horizontal line), the equation becomes y = y₁. For undefined slope (vertical line), it becomes x = x₁.

Q5: Can I use this for non-linear equations?
A: No, point-slope form only applies to straight lines (linear equations).