Graphing linear equations in two variables calculator

Graphing Linear Equations represents the graph of the given linear equation. As it always results in the form of a straight line. We generally use the graphical form of representation to prove the relationship between two or more quantities. The graph of the linear equations with two variables is a line. 

One of the most important concepts of algebra is Graphing Linear Equations. To graph the equation, it should be in the form of y = mx + b, also known as the y-intercept form, where m is the slope of the equation. 

Steps for Solving Graphical Linear Equations

Solving the linear equations graphically and represented in a coordinate plane is called graphical linear equations. The steps that should be followed to solve a linear equation using the graphical method are listed below: 

• Firstly, ensure the given linear equation is in y-intercept form, ie., y = mx + b. 
• Now, go with the trial and error method and find the value of (x,y) upto three pairs, which meet the linear equation.
• Calculate the x-intercept and y-intercept of the equation. Substitute the value of x=0 in the equation to find the y-intercept and its outcomes in x=a. For the sake of x-intercept, substitute the value of y=0 in the equation and result in y=c.
• As a result, the points are (a, 0) and (0, c). Now, put the value of x and y in a tabular form. 
• In this step, you have to plot all the points on the graph.
• Now, it's time to join all the points and obtain the straight line representing the given linear equation graphically. 

Example: 

Draw the linear equation of 2x+y=7 graphically? 

Solution:

Given equation is 2x+y=7

Rearrange the given linear equation in the form of y = mx + b ie., y = -2x + 7

You can find two solutions, corresponding to the x-intercepts and y-intercepts of the graph, by setting the first x=0 and then y=0.

When x=0, we get:

y = -2(0) + 7

y = 7

When y=0, we get: 

-2x+7=0

-2x = -7

-x = -7/2

x = 3.5

The coordinates of the plane are (0, 7), (3.5, 0) for the given linear equation 2x+y=7. The graphical representation of the linear equation is shown below.

Going from a linear equation to a line on a graph is like finding a hidden path. To reveal the path, we only need two points, which we can get using the equation.

Try it out to see for yourself! 😏

Line:

Starting at , where should we move to get on the path?

If we plug in a

horizontal position (-value)

, the equation will tell us what our

vertical position (-value)

needs to be in order to get to a point on the path. We like to start with the y-intercept.

We can then use the slope or plug in a second

-value

to get another point on the line and reveal the direction in which we need to keep moving to stay on the line.

Once we have two points, we can connect the points to reveal the full path of the line.

The Y-Intercept

The -intercept is the point where the line crosses the y-axis.

We can find the -intercept by plugging in . If the equation is in slope-intercept form (

), the

-value

The Slope

Slope measure the

change in (rise)

change in (run)

If the equation is in slope-intercept form (), the slope is equal to .

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How do you graph a linear equation in two variables?