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
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.Try the free Mathway calculator and
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