1. What is the Point-Slope Formula?

The point-slope formula is a linear equation that describes a line using a known point on the line and the slope of the line. It provides a way to find the y-value for any given x-value on the line.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

Where:

• \( y \) — Dependent variable (unitless)
• \( y₁ \) — Y-coordinate of known point (unitless)
• \( m \) — Slope of the line (unitless)
• \( x \) — Independent variable (unitless)
• \( x₁ \) — X-coordinate of known point (unitless)

Explanation: The formula calculates the y-value for a given x-value using a known point (x₁, y₁) on the line and the slope m.

3. Importance of Point-Slope Calculation

Details: The point-slope form is essential in algebra and coordinate geometry for writing equations of lines, making predictions, and solving linear relationship problems.

4. Using the Calculator

Tips: Enter the coordinates of a known point (x₁, y₁), the slope of the line (m), and the x-value for which you want to find the corresponding y-value. All values are unitless.

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 uses the y-intercept and slope. Both can represent the same line.

Q2: Can I use this formula for vertical lines?
A: No, vertical lines have undefined slope and cannot be represented using the point-slope formula.

Q3: What if I have two points instead of a point and slope?
A: You can calculate the slope first using (y₂ - y₁)/(x₂ - x₁), then use the point-slope formula with either point.

Q4: Are there limitations to this formula?
A: The formula only works for linear relationships and cannot be used for curves or non-linear functions.

Q5: Can this be used for real-world applications?
A: Yes, the point-slope formula is widely used in physics, economics, engineering, and other fields to model linear relationships.