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)
• \( y_1 \) — 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 formula calculates the y-value for a given x-value based on a known point (x₁, y₁) and the slope m of the line.

3. Importance of Point-Slope Calculation

Details: The point-slope form is essential in algebra and coordinate geometry for defining linear relationships, predicting values, and understanding the behavior of linear functions.

4. Using the Calculator

Tips: Enter the coordinates of the known point (x₁, y₁), the slope of the line (m), and the x-value for which you want to calculate y. All values should be numeric.

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 (y = mx + b) uses the slope and y-intercept.

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

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

Q4: Are there limitations to this formula?
A: The formula only works for linear relationships and requires that the slope is defined (not vertical).

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