Equation From Two Points Calculator

Line Equation Formula:

\[ y - y_1 = m(x - x_1) \] \[ \text{where } m = \frac{y_2 - y_1}{x_2 - x_1} \]

Slope-Intercept Form:

Point-Slope Form:

Standard Form:

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1. What is the Equation From Two Points?

The equation from two points calculates the linear equation that passes through both given points in a 2D plane. This is a fundamental concept in algebra and coordinate geometry.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ \text{Slope (m)} = \frac{y_2 - y_1}{x_2 - x_1} \] \[ \text{Slope-Intercept Form: } y = mx + b \] \[ \text{Point-Slope Form: } y - y_1 = m(x - x_1) \] \[ \text{Standard Form: } Ax + By = C \]

Where:

\( (x_1, y_1) \) — First point coordinates
\( (x_2, y_2) \) — Second point coordinates
\( m \) — Slope of the line
\( b \) — Y-intercept

3. Importance of Line Equations

Details: Line equations are essential in mathematics, physics, engineering, and computer graphics for modeling relationships between variables and representing linear trends.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will provide the equation in slope-intercept, point-slope, and standard forms.

5. Frequently Asked Questions (FAQ)

Q1: What if my points create a vertical line?
A: Vertical lines have undefined slope and are represented as x = constant.

Q2: What if my points create a horizontal line?
A: Horizontal lines have zero slope and are represented as y = constant.

Q3: Can I use this for 3D points?
A: No, this calculator is for 2D points only. 3D lines require vector equations.

Q4: How precise are the results?
A: Results are rounded to 2 decimal places for readability.

Q5: What if I enter the same point twice?
A: You need two distinct points to determine a unique line.