slope intercept straight line

The Slope and Intercept of a Line

The slope of a line is the ratio of change in a vertical distance over the change in a horizontal distance. It is denoted by m.


Process to find the slope of a line:

• We can take any two point on a line.
• Find the vertical change or change in y coordinate. 
• Find the horizontal change or change in x coordinate. 
• Find the ratio of these changes i.e. m = rise / run

We have basically 4 types of slopes. These are:

Zero Slope: In this case the line is parallel to the x axis, The value of x is change or increased, the value of y remains constant or unchanged.

Positive Slope: In this case as the values of x increase, the value of y is also increased and the slope of a line is positive.

Negative Slope: In this case as the values of x increase, the value of y is decreased and the slope of a line is negative.

No slope: In this case the line is parallel to the y axis, The value of y is change or increased, the value of x remains constant or unchanged.

Positive Negative Integers

Positive and Negative Integers

"The Integers" is a part of real numbers.

The Integer is a whole number, i.e. if the number is greater than 0 (zero) called the Positve Integers and those numbers less than zero called the Negative Integers. Zero is neither positive nor negative.

For every Positive Integer, there's exist a Negative Integer whihc is equal distance from the origin (0).
Two integers that lie the same distance from the origin and located in opposite directions from the orign are called the opposites. For example, "positive 9" (+9) is the opposite of "negative 9." (-9).

step by step solution substitution method

Substitution Method

 

Calculate value of x and y: Equations are y-x = 3 and 2(x + y) = 14


Solution:
In substitution method, we have a given equation of two variables, x and y.
First, divide in second equation by 2 in both sides.
x + y = 4 …. (1)
y – x = 3 => y = x + 3 ….(2)
Now, put the value of y in equation 1 and solve the equation for x, i.e
x + (x + 3) = 4
x + x + 3 = 4
2x = 4 –3
which gives x = 1/2.

Now, substitute x = 1/2 in any one of the given equation and find the value of y
y = 1/2 + 3
y = 7/2
Answer is : x = 1/2, y = 7/2

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Mean Median Mode Formulas

Mean: The "mean" is the "average" of given numbers. To find the mean, you just add up all the numbers and then divide by the number of numbers.

Median: The "median" is the "middle" value in the list of numbers. To find the median, your numbers, first list all the given numbers in ascending or descending order, and then find the middle term in the arrangement.   

Median:The "mode" is the value that occurs most often.

Range: The "range" is just the difference between the largest and smallest values.

For Example: The mean, median, mode and range of 2,1,3,6,9,8,3,6,3,0,1,6 are: 

To Find the Mean just add up all the numbers and divide it by number of total numbers i.e. 

               Mean = (2 + 1 + 3 + 6 + 9 + 8 + 3 + 6 + 3 + 0 + 1+ 6)/12

                        = 48/12  

                        = 4

To find the median, first set up all the given numbers in ascending order i.e. 

       

       0, 1, 1, 2, 3, 3, 3, 6, 6, 6, 8, 9

Median is the Middle value, i.e average of 6th and 7th term

         Median : (3 + 3)/2 = 3

To find the mode, you just see which number is appearing mostly in a given list of numbers.

0 - One times

1 - Two times

2 - One times

3 - Three times

6 - Three times

8 - One times

9 - One times

Mode is : 3 and 6


Range: Highest number- smallest number : 9 - 0 = 9

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Elementary Algebra

Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations such as +, −, ×, ÷

A polynomial is an expression that is constructed from one or more variables and constants, using operations of addition, subtraction, and multiplication. For example, x²- 7x − 1 is a polynomial in the single variable x.

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Meaning of Operation Research

Meaning of Operation Research

There have been various definitions for Operation Research 

Operation research is the application of scientific methods, techniques and tools to problems involving operations of systems so as to provide those in control of operations with optimum solutions to given problems. 

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Parallel and Perpendicular Lines

Two lines with the same slope are said to be a parallel lines. When we plot a graph of parallel lines then they will never intersect to each other. Line AB and Line CD are Parallel lines and it is denoted by AB||CD.

The equation of the straight lines are y = m1x + c and y = m2x + c are parallel  if the slopes of both lines are equal i.e.  m1 = m2 and the lines are perpendicular lines if m1m2 = -1.

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