Forms on linear Functions

A linear function is a polynomial function of first degree with one variable.The standard form of linear functions is written as f(x)= mx + b.

A linear function is represented in a cartesian plane by a straight line. 


Slope intercept form of a line:
y = mx +b is the slope intercept form of a line where x and y are coordinates of any point on the line,m is the slope of the line and b is the y-intercept.

Slope point-form of a linear function:

(y - y1) = m(x - x1) is the slope-form of a line.

Intercept form of a linear function:

(x/a)+(y/b) = 1 is the intercept form of a linear function.

Let us take an example on form of linear function.If a linear function is defined as 10x-5y+15=0, how to we express the function in slope-intercept form.
Soln.10x-5y+15=0
     or -5y=-10x-15
     or y=2x+3  
So, the slope intercept is y=2x+3.


Next time we will learn about differentiability of a function.
See more examples on how to write a linear function in different forms from free help on solved examples.

Vector

What is a vector?

A vector is a physical quantity which has a direction. Velocity and acceleration are examples of vector.

Types of vector:

Null vector or zero vector:A vector whose initial and terminal points are coincident is called a zero or null or a void vector.  a  = AB is the presentation of null vector.

Proper vector:Vectors other than the null vector are called proper vectors.

Unit vector:A type of  vector whose modulus is unity, is called a unit vector.

Negative of a vector:

  
The negative of a vector AB is a vector whose magnitude  is the same as that of vector AB but has the direction opposite to it.

Thus AB represents the vector of vectors a

= > BA represents −a

 

Learn calculus

The key concepts in calculus are integral calculus and differential calculus.

Differential calculus is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behaviour of functions. This can be illustrated by the slope  of a function's graph.Integral calculus studies the accumulation of quantities, such as areas under a curve  linear distance traveled, or volume  displaced.

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Calculus has widespread application in areas like Engineering and Science. Since the study of Calculus is pivotal in branching out to other fields, it is important to get the best Calculus help right from the formative years itself.

Geometric sequence

A geometric series is a series with a constant ratio between successive terms. For example, the series

1/2+1/4+1/8+1/16+.......is geometric, because each term  except the first can be acquired by multiplying the  first term by 1/2.

 

Geometric sequence:

A arrangement in which each term after the first  is a constant multiple of the  preceding  term is a geometric sequence.For example, The sequence, 2, 6, 18, is geometric since the arrangement between two adjoining  terms is consistently 3. That is, each term multiplied by 3 will produce the next term.

The accepted term of a geometric sequence (an) with a first term of a1 and a common ratio of r is an = a1(r^n-1).

Classification of algebra

In mathematics, algebra is concerned with the study of rules of operations and relations .Algebra is one of the main branch of mathematics.

Classification of algebra.
Algebra is classified as - elementary
                                   - abstract
                                   - linear
                                   - universal
                                   - algebraic number theory
                                   - algebraic geometry
                                   -algebraic combinatorics
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We will go through all the types of algebraic concepts with examples of problems solving.There are experts who give online algebra help through different websites.

Algebra is used in many areas in our daily life.It is used in business,schools for maintaining students' report, in reading temperature in thermometer, etc.

Online tutor

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Trigonometry

Trigonometry is the science of relations between angles and sides of triangles.There are many formula in trigonometry.

Some basic formula are: In a triangle with sides A, B and C,
                                                                                            Sine A = Opposite/Hypotenus
                                                                                            CosA = Adjacent/Hypotenus
                                                                                             Tan A = Opposite/Adjacent
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Application of basic formula will also be taught with many examples.


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Trigonometry functions are used for navigation, engineering and physics.Next time we learn how to
solve different problems of trigonometry.