1. What is the Point-Slope Formula?

The point-slope formula is a method for finding the equation of a line when you know the slope and one point on the line. It's expressed as y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the known point.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

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 formula directly relates the difference in y-values to the difference in x-values through the slope.

3. Importance of Point-Slope Form

Details: The point-slope form is particularly useful when you know one point on a line and its slope. It provides a straightforward way to write the equation of a line without needing the y-intercept.

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: What if my slope is zero?
A: A zero slope indicates a horizontal line. The equation will be y = y₁ (a constant value).

Q2: What if my slope is undefined?
A: An undefined slope indicates a vertical line. The equation will be x = x₁ (a constant value).

Q3: How is this different from slope-intercept form?
A: Point-slope form uses a specific point, while slope-intercept form (y = mx + b) uses the y-intercept. They can be converted between each other.

Q4: Can I use this with decimal values?
A: Yes, the calculator supports decimal values for all inputs.

Q5: What if I have two points instead of one point and slope?
A: You would first need to calculate the slope using the formula m = (y₂ - y₁)/(x₂ - x₁), then use one of the points with the point-slope formula.