1. What is the Point-Slope Formula?

The point-slope formula is a method to find the equation of a line when you know the slope and one point on the line. It provides a straightforward way to express linear relationships in mathematics.

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 equation of a line by relating the difference in y-values to the difference in x-values through the slope.

3. Importance of Point-Slope Formula

Details: The point-slope form is essential in algebra and coordinate geometry for finding linear equations, graphing lines, and solving problems involving linear relationships.

4. Using the Calculator

Tips: Enter the slope value, and the coordinates of the known point. The calculator will provide both the point-slope form and the simplified slope-intercept form of the equation.

5. Frequently Asked Questions (FAQ)

Q1: When should I use point-slope form instead of slope-intercept form?
A: Use point-slope form when you know a point on the line and the slope, but not the y-intercept.

Q2: Can I convert point-slope form to standard form?
A: Yes, by rearranging the terms to get Ax + By = C format.

Q3: What if my slope is zero or undefined?
A: For zero slope (horizontal line), the equation becomes y = y₁. For undefined slope (vertical line), the equation becomes x = x₁.

Q4: Are there limitations to this formula?
A: The formula only works for linear relationships and requires knowing both the slope and one point on the line.

Q5: Can this be used for non-linear equations?
A: No, the point-slope formula is specifically designed for linear equations only.