Equation of a Line Calculator

The equation of a line calculator is used to plot and compare two lines or more than two to each other. The line equation from two points calculator shows the set of data that makes a line in a coordinate system. 

What is the Equation of a line?

In an algebra form, the equation of a line indicates the set of points that combine together to make a line. It also represents all points that lie on the cartesian coordinates. 

Standard Forms of Line Equation:

Find equation of a line in its general form and in its corresponding relationships. There are three main types of a linear equation that are as follows:

• Point slope form
• Slope intercept form 
• Standard form 

1. Point Slope Form:

The equation that makes by drawing the one point and slope of a line. This equation is known as the point-slope form. Their equation can be written as:

y – y1 = m(x – x1) 

Where:

• X1 and Y1 = Starting and ending points of a line 
• m = Slope of a line 

The slope is the rise over run when the point form is written as (x, y) or it is available as a change in the ratio of y over the change in ratio of x. Put the value of one point and slope m in the equation of a line calculator and get the answer easily. 

Example:

Assume the point on the x-axis and the y-axis are (4, 5) and slope m is equal to 7. How to find the equation of a line with two points for point-slope? 

Given Data:

X1 = 4
Y1 = 5

y – y1 = m(x – x1) 

y - 5 = 7(x - 4)

2. Slope Intercept Form:

The method at which the slope and the intercept at the line cross the vertical y-axis which is apparent. The equation is written as:

Y = mx + c 

Where:

• Y = slope intercept form
• m = slope of a line 
• c = y-intercept of the equation

Example:

Suppose a line the “m” slope is equal to the 7 and y-intercept is equal to 9 so evaluate the slope interception of that line. 

Hence, this problem can be made easy with the equation of a line calculator. So we write an equation of the line that passes through the points.

Y = mx + c 

So after inserting the values, the equation will be:

Y = 7x + 9

3. Standard Form:

In order to describe small or large terms concisely a standard form is used. This form of line can be written as follows:

Ax + By = C

Also, this equation is written as:

Ax + By + C = 0

Where:

• A and B = Coefficients of variables of x and y 
• C = y-intercept of a line 

Example: 

How to find the equation of a line with one point by using the point-slope or slope-intercept form. In order to evaluate the standard form so let us take a slope intercept form that is: 

Y = 7x + 9

Apply the operations:

⇒    7x+9-y=0

⇒    7x-y+9=0

In the final, we conclude the standard form:

7x-y=-9   

How to Find the Intercept of a Line?

An equation of a line that passes through two points and the intercept is of two types x and y. These intercepts help us to plot a graph. So get the graph by the below calculations. 

Y-intercept of Line Equation:

The value of y where the verticle line crosses the y-axis is known as the y-intercept. Calculate the y-intercept when the value of x = 0. To find an equation of the line put the values in the equation of a line calculator and get:

y = mx + c 

This equation indicates all points that lie on the line so insert the value of x. 

y = 2x – 9

y = 2(0) – 9

y = 0 – 9

y = – 9

X-intercept of Line Equation:

The value of the x where the perpendicular line crosses the x-axis is known as the x-intercept. Calculate the x-axis when the value of y = 0 so put the value in the equation from two points calculator and get;

y = mx + c

0 = 2x + ( -9)

2x = 9

x = 9/2

Slope of Parallel and Perpendicular Lines: 

The lines that are equal at the same plane and never intersect each other a parallel line and on the other side, the lines intersect at a right angle. So according to the definitions, we say that the parallel lines have the same slope and the perpendicular lines have the opposite slope.

This line equation calculator helps us to write the equation of a line passing through any pair of points.

Where:

m=ab, m⊥=−ba

Hence, find the slopes whether the slope is perpendicular or parallel to each other by the line equation from two points calculator.

Working of Equation of a Line Calculator:

This equation of the line calculator determines the line equation that depends on the various parameters by keeping in account the following points:

Input:

• Select the option that you want to calculate
• Insert the values in the designated field of the tool 
• Tap “Calculate”

Output:

Our equation of line calculator will give you the following results:

• General equation form 
• A detailed solution with steps shown 
• Graphic representation of values 

References:

From the source Wikipedia: Linear equation, Different variables. 

From the source chilimath: Ways to Plot a Graph.