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Equation Of A Line From Two Points On The Line




 
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More Lessons for Geometry

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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:

slope formula

Example:

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

Solution:

Step 1: Calculate the slope.

    slope = change in y / change in x= slope values

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




The following video shows how to use the slope formula to calculate the slope of a linear equation given two points.

The following video shows 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.



Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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