Point Slope Equation From 2 Points Calculator

Point Slope Equation:

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

Point Slope Equation:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Point Slope Equation?

The point slope equation is a linear equation form that describes a line using a known point on the line and the slope of the line. It is expressed as y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

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 takes two points (x₁, y₁) and (x₂, y₂), calculates the slope m, and generates the point slope equation using the first point.

3. Importance of Point Slope Form

Details: The point slope form is particularly useful when you know a point on the line and the slope. It's commonly used in calculus, physics, and engineering applications where instantaneous rates of change are important.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will automatically compute the slope and generate the point slope equation. Ensure the points are not identical.

5. Frequently Asked Questions (FAQ)

Q1: What if the two points are identical?
A: The calculator will display an error because identical points cannot define a unique line (slope is undefined).

Q2: Can I use this for vertical lines?
A: No, vertical lines have undefined slope and cannot be represented in point slope form. They are represented as x = constant.

Q3: How accurate are the results?
A: The calculator provides results with 4 decimal places precision for the slope calculation.

Q4: What's the difference between point slope and slope intercept form?
A: Point slope form uses a specific point and slope, while slope intercept form (y = mx + b) uses the slope and y-intercept.

Q5: Can I use this for non-linear equations?
A: No, the point slope form is specifically for linear equations only.