1. What is the Point-Slope Form?

The point-slope form is a linear equation format that describes a line using a known point (x₁, y₁) on the line and the slope (m) of the line. It is expressed as: y - y₁ = m(x - x₁).

2. How Does the Calculator Work?

The calculator uses the point-slope form equation:

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: This form is particularly useful when you know one point on the line and the slope, allowing you to write the equation of the line directly.

3. Importance of Point-Slope Form

Details: The 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 particularly useful in real-world applications where rate of change (slope) and a specific data point are known.

4. Using the Calculator

Tips: Enter the coordinates of the known point (x₁, y₁) and the slope (m) of the line. The calculator will generate the complete point-slope form 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 necessarily the y-intercept. It's more direct than converting through other forms.

Q2: Can I convert point-slope form to slope-intercept form?
A: Yes, by solving for y: y = m(x - x₁) + y₁, which simplifies to y = mx + (y₁ - mx₁).

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: Can I use this form with decimal or fractional values?
A: Yes, the calculator handles decimal values. For fractions, you may want to simplify the equation after calculation.

Q5: How accurate is the point-slope form calculation?
A: The calculation is mathematically precise based on the inputs provided. The accuracy depends on the precision of your input values.