1. What is the Point-Slope Equation?

The point-slope equation is a linear equation form used to describe a line when you know the slope and one point on the line. It is 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 equation:

Where:

• \( y \) — Dependent variable (unitless)
• \( y₁ \) — Y-coordinate of known point (unitless)
• \( m \) — Slope of the line (unitless)
• \( x \) — Independent variable (unitless)
• \( x₁ \) — X-coordinate of known point (unitless)

Explanation: The equation shows the relationship between any point (x, y) on the line and the known point (x₁, y₁) using the slope m.

3. Importance of Point-Slope Form

Details: The point-slope form is particularly useful when you have a point and the slope, making it easier to write the equation of a line without needing to convert to other forms like slope-intercept form.

4. Using the Calculator

Tips: Enter the y-coordinate of the point (y₁), the slope (m), and the x-coordinate of the point (x₁). All values should be numerical.

5. Frequently Asked Questions (FAQ)

Q1: What is the point-slope form used for?
A: It is used to write the equation of a line when you know the slope and one point on the line.

Q2: How is point-slope form different from slope-intercept form?
A: Slope-intercept form is y = mx + b, which requires knowing the slope and y-intercept. Point-slope form uses the slope and any point on the line.

Q3: Can I use point-slope form with any point on the line?
A: Yes, any point on the line can be used with the slope to write the equation in point-slope form.

Q4: How do I convert point-slope form to slope-intercept form?
A: Distribute the slope and then solve for y to isolate it on one side of the equation.

Q5: What if the slope is zero?
A: If the slope is zero, the line is horizontal, and the equation simplifies to y = y₁.