1. What is Point Slope Form?

The point-slope form is a way to express the equation of a line when you know the slope and one point on the line. It's particularly useful in algebra and calculus for writing linear equations quickly.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

Where:

• \( m \) — Slope of the line
• \( (x_1, y_1) \) — Known point on the line

Explanation: The equation shows that the difference in y-values between any point (x,y) and the known point (x₁,y₁) is proportional to the difference in x-values, with the slope as the constant of proportionality.

3. Importance of Point Slope Form

Details: Point-slope form is essential in algebra for quickly writing equations of lines, especially when given a point and slope. It's also useful for finding tangent lines in calculus and modeling linear relationships in various fields.

4. Using the Calculator

Tips: Enter the slope (m) of your line and the coordinates (x₁,y₁) of a point the line passes through. The calculator will provide both the point-slope form and the slope-intercept form of the equation.

5. Frequently Asked Questions (FAQ)

Q1: When should I use point-slope form?
A: Use it when you know the slope of a line and one point it passes through, especially when you need to quickly write an equation.

Q2: How is this different from slope-intercept form?
A: Slope-intercept form (y = mx + b) shows the slope and y-intercept explicitly, while point-slope form shows the relationship between any point and a specific known point.

Q3: Can I use this with two points instead of slope and point?
A: Yes, but you'd need to calculate the slope first using (y₂ - y₁)/(x₂ - x₁) before using the point-slope form.

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

Q5: How do I graph using point-slope form?
A: Plot the known point (x₁,y₁), then use the slope to find additional points by moving up/down (numerator) and left/right (denominator) from that point.