1. What is the Point-Slope Form?

The point-slope form is a linear equation format that describes a line using its slope and a single point on the line. The general form is: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

2. How Does the Calculator Work?

The calculator uses the point-slope form equation:

Where:

• \( m \) — Slope of the line (unitless)
• \( x_1 \) — X-coordinate of the known point (unitless)
• \( y_1 \) — Y-coordinate of the known point (unitless)
• \( x \) — Independent variable (unitless)
• \( y \) — Dependent variable (unitless)

Explanation: The calculator accepts fractions as input and displays the resulting equation in proper mathematical format with fractions preserved.

3. Importance of Point-Slope Form

Details: Point-slope form is particularly useful when you know one point on the line and the slope. It's commonly used in calculus, physics, and engineering applications where precise linear relationships need to be expressed.

4. Using the Calculator

Tips: Enter the slope value (can be a fraction like 2/3), the x-coordinate of the point (can be a fraction), and the y-coordinate of the point (can be a fraction). The calculator will generate the complete point-slope form equation.

5. Frequently Asked Questions (FAQ)

Q1: Can I enter decimal values instead of fractions?
A: Yes, the calculator accepts both decimal values and fractions. However, fractions will be preserved in the output for mathematical clarity.

Q2: What if my slope is zero?
A: A zero slope indicates a horizontal line. The equation will simplify to y = y₁.

Q3: How do I convert point-slope form to slope-intercept form?
A: Distribute the slope through the parentheses and solve for y: y = m(x - x₁) + y₁.

Q4: Can I use negative fractions?
A: Yes, negative fractions are supported. For example, -3/4 is a valid slope input.

Q5: What if I get an undefined slope?
A: For vertical lines (undefined slope), point-slope form cannot be used as the slope is undefined. You would use x = x₁ instead.