# Equation Of A Line From Two Points On The Line

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In this lesson, we will learn how to find the equation of a line when given two points on the line. We will also learn how to determine the equation of a vertical line or a horizontal line given two points on the line.

To find the equation of a line when given two points on the line, we first find the slope and then find the y-intercept.

The slope is the ratio of the change in the y-value over the change in the x-value. Given any two points on a line, you can calculate the slope of the line by using this formula:

Example:

Given two points, P = (0, –1) and Q = (4,1), on the line, find the equation of the line.

Solution:

Step 1: Calculate the slope.

slope = =

Step 2: Substitute m = , into the equation, y = mx + b, to get the equation

Step 3: Select one of the given points, for example (4, 1), and substitute the x and y values into the equation.

We, then, get that b = −1, which is the y-intercept.

Step 4: Subtitute b = −1 to get the equation.

y = x − 1

How to use the slope formula to calculate the slope of a linear equation given two points. How to find the equation of a line given two points on the line?

### Equation of a Vertical Line

This video explains how to determine the equation of a vertical line given two points on the line.

### Equation of a Horizontal Line

This video explains how to determine the equation of a horizontal line given two points on the line.

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