Two Points Line Equation Calculator

What is a Line Equation Through Two Points?

A line equation through two points is a mathematical formula that describes a straight line passing through two specific points in a coordinate plane. It's like drawing a straight line between two dots on a graph paper! This equation helps us understand the relationship between any two points on that line.

How to Find a Line Equation Through Two Points

To find the equation of a line through two points, we use the point-slope form or the two-point form. It's a simple process that involves the coordinates of both points and a bit of algebra. Let's see how it works!

Formula

The two-point form of a line equation is:

\[ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} \]

Where:

• \((x_1, y_1)\) is the first point
• \((x_2, y_2)\) is the second point
• \((x, y)\) is any point on the line

Calculation Steps

1. Identify your two points \((x_1, y_1)\) and \((x_2, y_2)\)
2. Calculate the slope using: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
3. Use point-slope form: \(y - y_1 = m(x - x_1)\)
4. Simplify to get \(y = mx + b\) form
5. Convert to standard form if needed: \(Ax + By + C = 0\)

Example and Visual Representation

Let's find the equation of a line through points (2, 3) and (5, 7).

The blue line in our graph shows the final result - a straight line passing through both points. The red dashed lines show how we calculated the slope by counting the rise (vertical change) and run (horizontal change). This visual representation helps us understand how the slope \(\frac{4}{3}\) relates to the actual line on the graph!