Graphing Linear Equations and Functions

Introduction

Linear equations are relation between two variables. Generally in form of ax+by+c = 0 or ax+by = c. We can see linear functions also. These are nothing but similar to linear equations. Generally a function can be in form of f(x) = ax + b, we can write this function as y = ax + b also.

Now graphing linear equations and functions are very simple. Since these are a straight lines, you have to just find two points through which these lines passes and once you find the point you can draw a line meeting both the point. Here are steps for graphing equations and functions.

Steps for Graphing Linear Equations and Functions

Step1: Put x=0, you will get value of y, lets say y = b, first point will be (0,b)

Step2: put y=0, you will get value of x, lets say x = a, second point will be (a,0)

Step3: Plot both the points and draw a line meeting both the points and extend this line beyond these points.

In this way you will get required graph of linear equation and functions.

Following examples help you in understanding these steps and similar problems.

Examples for Graphing Linear Equations and Functions

Ex:1 Graph the linear equation: 2x + y = 6

Put x=0, we get y =6

first point wil be (0,6)

Put y=0, we get x=3

second point will be (3,0)

Now plot these points and draw the required graph of this linear equation.

Understanding algebra 2 help online is always challenging for me but thanks to all math help websites to help me out.

Ex:2 Graph the function f(x) = 4x + 4

put in the form of y = 4x + 4

Put x = 0, we get y = 4, First point will be (0,4)

Put y = 0, we get x=-1, second point will be (-1,0)

Now plot the points and draw the graph.

Introduction of sample proportion

Introduction of sample proportion:

          Two equal ratios form a proportion. Thus, if a:b=c:d then a,b,c,d are said to be sample proportional. We write this as, a:b::c:d. This is read as “a is to be is as c is to d”A and b are called the extremes and b an c are called the means. The terms d is called the fourth sample proportional to a,b,c.

Types of Sample Proportions:

Continued proportion: quantities a,b,c,d,…. Are said to be in continued proportion if, a/b=b/c=c/d….. i.e., a:b=b:c=c:d=……………….

Mean proportional:  consider a,b, and c are in continued proportion, Proportion will be represented as a:b::b:c. Here, b is called the mean proportional of a and c..

Also c is called the third proportional to a and b.. If a,b, c are in continued proportion, then ac:b² . Hence, if three quantities are in continued proportion, then the product of extremes is equal to the square of the mean.

Note: The product of the extremes is equal to the product of the means.

Inadvertent: If a:b::c:d, then, b:a::d:c. for, a/b=c/d gives a/c=b/d. This operation is called inadvertent. It says that if quantities are proportion they are also proportional when we take it inversely.

Alternendo: if a:b::c:d then a:c::b:c.

For, a/b=c/d gives a/c=b/d. This operation is called alternendo. It says that if four quantities are proportional, they are also proportional when taken alternatively.

Componendo: If a:b::c:d, then (a+b):b:(c+c):d.

Given that, a/b=c/d,

So,(a/b)+1=(c/d)+1

Or, (a+b)/b=(c+d)/d

This operation is called componendo.

Dividendo: If a:b::c:d,

Then (a-b):b::(c-d):d.

Given that, a/b=c/d,

So,(a/b)-1=(c/d)-1

Or, (a-b)/b=(c-d)/d.

This operation is called dividendo.

Componendo and Dividendo:

If a:b::c:d,

Then (a+b):(a-b)::(c+d):(c-d).

Using componendo and dividendo respectively, we get

(a+b)/b=(c+d)/d   -------------------------1

(a-b)/b=(c-d)/d.    -------------------------2

Dividing the respective sides of 1 by those of 2 we get

(a+b)/(a-b)=(c+d)/(c-d)

This operation is called componendo and dividendo.

Examples for Finding the Sample Proportion:

Ex 1  : 2/5=4/10

Sol :  2/5=4/10

If we do the cross multiplication, we will get

5*4 = 2 *10

20 = 20 so, : 2/5=4/10 is a proportion.

Ex  2:  2/5=4/10

Sol :    1/5=4/10

If we do the cross multiplication, we will get

5 X4 = 1 X 10

20 = 10 so, : 1/5=4/10 is not a proportion.

Geometry Math Project

Introduction to Geometry Math Project:

              A geometry math project is an interesting assignment (project) work which tends the student to work independently and let them analyze the mathematical observations to find the valuable solution which may be a new invention or change of the existing one. It improves the student’s knowledge in the Geometry and tends them to develop new formulas and make them solve the critical problems. Geometry is a division of Mathematics, which also suits everyone to face their life problems.
             
A Geometry Math Project

              Geometry is the major part of the mathematics that deals with the size, shape, relative position of figures, and the properties of space. There are many types of problems in geometry. When students involve in doing the geometry project, they have to choose the major topic and make themselves involved in the topic.

          
Steps to be followed to do a geometry math project

   To do a geometry math project, students have to follow the below steps.  
•    They have to choose the major subject from the geometry divisions in mathematics.
•    After the topic was chosen, the students have to start collecting the complete details of the subject.
•    Details may include the failures and the mistakes occurred during the time of calculation and they have to study about each sub topic to analyze the data.
•    After understanding about the topic, they have to do some experiments with the help of sample problems. Sample problems should cover all the formulas that have to be modified. 
•    In the experiment, they can use pictures, graphs or drawings to enhance their presentation.
•    Finally they have to give complete details about the topics like definition, properties, characteristics, etc.
•    By completing the experiments, students have to see the changes with the help of the existing project and have to prepare a report.

Completing the Geometry Math Project

              In any project, the final report takes a major part which helps them to complete the project in a successful way and they have to prepare a presentation on the project title. The final decision of the project may be applicable in real-time  situation.

Algebra made easy here !

Let's gain a quality learning of algebra through today's post specifically concerning with algebraic expressions.

Algebra is the study of expressions and variables. The main operation with algebra is finding the real numerical value of algebraic expressions. Usually algebraic expressions are represented as for example: 2x+3y = 0. Here, x and y are the unknown variables. These unknown variables are also termed as algebra symbols. Algebra symbols are very important in the study of algebra.

Other symbolic representation in algebra are: equivalence, approximate to, greater than and less than, parentheses, brackets, braces and so on.

For more help with this, connect with an online tutor and get your required help. You can connect with free algebra tutoring and learn the concept with better hand.

Do post me back your feed backs.

Learn to mulitply fractions with me

Learn how to multiply fractions in today's post. Multiplying fractions is the easiest of all mathematical operations of fractions.

Multiplying fractions unlike adding and subtracting fractions with unlike denominators doesn't involve finding LCM. While multiplying fractions, the numerator should be multiplied by the numerator and the denominator should be multiplied by the denominator.

As for example: Multiply 2/3 * 5/6 = 10/18 = 5/9

For more help with this, one can avail to an online tutor and get the required help. Not just fractions help but one can opt for calculus tutoring and others as well.

Next time we will move on learning some other concept. Till then understand this concept and do practice problems to improve.

joint probability density function

We have already worked on how to do probability problems isn't it? We solved many probability problems, probability quiz and many things in probability.

I have worked on various problems till date, you will have to look for my previous post which is related to probability to understand the concept of the day. I have tried to increase your knowledge in probability.

Lets work on joint probability density function below.

Joint probability density is said to be method of learning the random variable of the probability density function. If the variables A and B are random variables and it has a probability density function.

Here you have read joint probability density function and we will work on problems related to it.

Also you can follow my blogs for volume formula. I hope this was useful.

simplest form calculator

Today guys i have a simple definition for simplest form calculator, check out...

Simplest form calculator is used to calculate the equations or quantitative values in simplest modify. Using the simplest work expert, essential arithmetic fractions can be done. These calculators are very effectual for solving slaty cipher problems. The simplest form calculator calculates the answer and displays it.

Find an example below.

Example 1:

Solve the fraction, 4/9 + 2/9

Solution:

In this given problem the denominators are same; hence just perform the addition operation.

= 4/8+ 2/9

= 4+2/9

= 6/9

Simplify it,

= 2/3

The answer is 2/3 .

I will come back with factoring polynomials calculator shortly...

Also you can follow my blogs for Free algebra answers. I hope this was useful.