# Archive for June, 2012

## How to tackle Linear Function

We all study about many types of the functions in the context of the math for example the rational function, the irrational function, the greatest integer function, the modulus function and various types of the functions of the trigonometry so in this article we will also discuss about one of such a function which most of us know about and also generally encounter while studying the math that is the **linear function**. We all generally speak about the linear function and also solve some of their problems but many of us are not even aware of the perfect explanation of this type of the function so this article will us understand this function very clearly. (Know more about Linear Function in broad manner, here,)

The linear function has got different types of the definitions in the context of the math for example it has got one definition from the general math while it has got some other meaning under the geometry which is analytical and also the vector spaces define this type of the function in a different manner. So in this article we will concentrate only on one of the definition of this type of the function which is very commonly used and is being given in the general math.

In the context of the general math the linear function can be associated with two different types of the meanings which are given as follows. The first meaning of this type of the function is that this function is a polynomial which is of degree one and which include only one type of the variable whereas the second meaning is the one in which this function refers to a map that is made with the help of the 2 vector spaces.

In order to get more help on the topics: Linear Function, **Bernoulli distribution** and cbse class 8 syllabus, you can visit various online portals which provide complete educational information.

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## What is a Linear Function

We all very frequently use the term linear function while studying the math but some of us do not know the exact meaning the term linear function so in this article we will discuss about **what is a linear function**. There is just not a single definition of the linear function in the math rather the linear function has got different types of the meanings in the different theories. So we will learn in each type of the theory about what is a linear function for example in the general math, in the geometry which is analytical and also in the vector spaces.

We will start with discussing about what is a linear function in the general math. In the general math the linear function can be linked with two distinct meanings. The first one is that the linear function is nothing but a function of the polynomial of a single degree and which consists of just single variable whereas in the second meaning the linear function is being referred to a map which is constructed the 2 vector spaces among which we can do the sum of the vectors and also their multiplication by a scalar. (know more about Linear Function, here)

We have discussed about what is a linear function in the general math so now we will discuss about what is a linear function in the geometry which is analytical. In the geometry which is analytical the linear function is also referred to a function of the polynomial of a single degree and which consists of just single variable but here these type of the functions are called linear as they are clearly those functions the graph of which when drawn in the Cartesian type plane of the coordinate comes out to be a straight line.

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## How to Graph Linear Equations

Now let us learn **how to graph linear equations**. For plotting the graph for the linear equation for one variable, we must remember that the line drawn will be a straight line parallel to one of three axis. Suppose we have any equation say:

X = 5, here we say that for any value of y, the value of x will remain same i.e. x = 5. So we say that the graph will be plotted at the following points: ( 5, 0 ), ( 5 , 1), ( 5 , 2 ), ( 5,3 ), ( 5,4 ) and so on. On plotting the graph we get the graph such that it is parallel to the y axis and will pass through x = 5.

Similarly if we have the equation y = 3, here we observe that the graph will be plotted such that whatever will be the value of x, the value of y will remain same i.e. y = 3, so we conclude that the graph will be parallel to x axis and will pass through y = 3. (know more about Linear equation, here)

If we have the equation as x + y = 5, then we say that the table will be first drawn to represent different values of x and the corresponding values of y. So we say that the different values of x and y can be taken and thus we are able to plot the graph based on these points. First we will mark these points from the table and then they are joined to plot the graph.

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## How to Solve Linear Equations

Let us learn about what linear equations are and **how to solve linear equations**. The equations which are in the form of ax + b = 0 or ax + by + c = 0 are called linear equations. The linear equation in the single variable can be solved by taking the variable of the equation to one side of the equation and the constants to the other side of the equation so that the value of the variable is attained, which is the solution to the given equation. By the word, solution to the given equation, we mean that the value of the variable is to be calculated, such that if we place that value of the variable in the equation, we find that the equation is satisfied. Now we look at the pair of the linear equations with the two variables. If we say that the equation has two variables say p and q, then the values of the variables is to be calculated, such that the both the values of the variables satisfies both the given equations. We can solve the pair of the linear equations graphically as well as by the algebraic methods. If we have to solve the linear pair of equations graphically in order to get the solution to the pair of the linear equations, we will first plot the graph of both the lines on the graph paper and observe the point of intersection of the two lines. This point of intersection is the solution of the given equation. (know more about Linear equation, here)

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