We will discuss about the Linear Equation. If you're learning about graphs, you're bound to see a bunch of linear equations, so it is a good idea to understand what makes an equation a Linear Equation. Now What Is a Linear Equation?

A Linear Equation is an Algebraic Equation in which each term is either be constant or the product constant. In simple mathematical terms we can say that any equation that when graphed produces a straight line is called a Linear Equation. Linear Equation can have one or more variables. It can be applied with great regularity in mathematics.

A common form of a linear equation in the two variables x and y is

y = ax + b, where a and b are the two constants. The origin name of linear comes in the forms of straight line in the plane. In this particular equation the m determines the slope of that line and b determines the point where the line cross the y-axis, and it is also known as y-intercept.

Linear Equation can be rewritten as using the laws of elementary algebra into several different form. These equation often knows as '' equation of the straight line'' in which x,y,and tan are variables.

The general form of a Linear Equation is Ax + By + C=0 , where b and a both are equal to zero.

The equation is written as A>0,A=0 means. The graph of the equation is a straight line and every equation

is a straight line in the form. If A is non zero then it is X-intercept means x-point where line crosses the x-axis point.

Now we take an example to solve the Linear Equation with the help of linear equation calculator, how to write a linear equation if its plot with the slope 4 passes through the point having the following coordinates: x1 = 3 and y1 =1. write the Linear Equation for the point with the coordinates x1 and y1;

y1= ax1 + b

in our example it will be

5 = 3a + b

now substract the equation in step 1 from the generic equation form

y = ax + b

y = ax + b

y1 = ax1 + b

-------------------

y - y1 = ax – ax1

Remembering that the coefficient a is the plot slope, you can write the equation in the slope-point form:

y - y1 = slope * (x - x1)

In our example, it is:

y - 5 = 4 * (x - 3)

Where a is the slope that is given. Hence it explicitly defines the coefficient b and allows you to write the Linear Equation as:

y = slope * x + b

In our example, the coefficient b would be:

b = 5 - (4 * 3) = 5 - 12 = -7

And the linear equation is:

y = 4x – 7

so hence the Linear equation has been solved by us and it would drive the solution of the linear Equation.

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This article was published on 2011/09/17

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## What is a linear equation and linear equation calculator?