Point Slope Calculator with Two Points

Point-Slope Formula:

\[ y - y₁ = m(x - x₁) \] \[ \text{where } m = \frac{y₂ - y₁}{x₂ - x₁} \]

Point-Slope Equation:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Point-Slope Formula?

The point-slope form is a linear equation format that describes a line using a known point on the line and its slope. It's particularly useful when you have two points and need to find the equation of the line passing through them.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

\[ y - y₁ = m(x - x₁) \] \[ \text{where } m = \frac{y₂ - y₁}{x₂ - x₁} \]

Where:

\( y \) — Dependent variable (unitless)
\( y₁ \) — y-coordinate of first point (unitless)
\( m \) — Slope of the line (unitless)
\( x \) — Independent variable (unitless)
\( x₁ \) — x-coordinate of first point (unitless)
\( y₂ \) — y-coordinate of second point (unitless)
\( x₂ \) — x-coordinate of second point (unitless)

Explanation: The calculator first calculates the slope using the two given points, then constructs the point-slope equation using the first point and the calculated slope.

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 you know a point on the line and its slope. It's particularly useful for finding tangent lines and linear approximations.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The x-coordinates must be different to avoid division by zero. The calculator will output the point-slope form equation using the first point provided.

5. Frequently Asked Questions (FAQ)

Q1: What if my two points have the same x-coordinate?
A: If x₁ = x₂, you have a vertical line. The calculator will show an error because vertical lines have undefined slope and cannot be represented in point-slope form.

Q2: Can I use this for any type of line?
A: Yes, for any non-vertical line. The point-slope form works for all lines except vertical ones.

Q3: How accurate is the calculation?
A: The calculation is mathematically exact. The result is rounded to 4 decimal places for readability.

Q4: What's the difference between point-slope and slope-intercept form?
A: Point-slope uses a specific point and slope, while slope-intercept uses the y-intercept and slope. They can be converted between each other.

Q5: Can I use this for 3D coordinates?
A: No, this calculator is designed for 2D coordinate geometry only.