How to Find the Equation of a Line

Hello friends today we are going to discuss the topic  How To Find The Equation Of A Line, for finding the equation of a line we need  to  have the knowledge of the three parameters  but before talking about the parameters we will be seeing that what actually is the equation of line,

Y = mx +c

(know more about Linear equation, here)

With the help of this equation we can the equation of line passing through two points with a slope, the direction of x will always be horizontal and the direction of y will always be vertical, in the above equation m is the slop of the given line, if a line passing through the origin then its equation will be

Y = mx

If the value of m is 3 then the equation of line is y – 3x = 0

Now suppose we are having two points as (x1, y1) and (x2, y2) and we are asked to find the equation of the line then we can find the equation of line as

y – y1= m (x – x1)

Here the value of m will be = y2 – y1 /x2 – x1

So we can rewrite our line equation as

y – y1 = (y2 – y1 /x2 – x1) * (x –x1)

if we have two points as (1,2) and (2,3) and we are asked two find the equation of line passing through these points then  the equation will be

y – 2 = m (x – 1)

Now we have to find the value of m, so the value of m will be

m = y2 – y1 /x2 – x1

m = 3-2 /2-1

m = 1

Now we will put the value of m in above equation,

y -2 = x -1

y –x =1

This is the required equation of line.

If you are going through, ICSE sample paper then please focus on word problem solver it is very important from exams point of view

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How to Define Altitude

In mathematics, altitude is a geometry word. It is defined as the height of an object or point in relation to sea level or ground level. In geometry, it is defined as the length of the perpendicular line from a vertex to the opposite side of a figure. Altitude is also known as height. It is the measurement of someone or something from head to foot or from base to top. It is said to be the elevation above ground. It is the height of an object above the horizon. Altitude has several definitions.

Altitude is used to find the area of a triangle. Altitude of a triangle is defined as the perpendicular line or line which passes to the base of a triangle and must be at right angle to the opposite sides. Area of a triangle is defined as the total space occupied by the surface of a triangle and area of a triangle is given by:

= ½ x base x altitude

Here, altitude is the length of the perpendicular line from the base to the opposite side of a triangle.

There are two conditions which should satisfy to find the altitude of a triangle:

1. Altitude must starts from a vertex.

2. Altitude must be perpendicular to the base of a triangle or a side of a triangle.

We don’t have altitude in square and rectangle because altitude is one of the sides of the figure.

Altitude is also useful in Factoring Polynomials Calculator.

Example:

Question:

Calculate the area of a triangle if base = 5 inch and altitude = 10 inch?

Answer:

Area of a triangle is given by:

=½ x base x altitude

=1/2 x 5 x 10 (inch)2

=10 (inch)2.

Last Altitude and Factoring Polynomials Calculator are also discussed in Tamilnadu Education Board.

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How to find Sphere Volume

A sphere is a round type of shape in three dimensions, it looks like a circle but it is very different from circle, like circle it also has radius and diameter. If we write the equation for circle then it would be x2 + y2 =a2. Here a is the radius of circle, as circle is a two dimensional shape so we have taken x and y and when we talk about sphere as we know well now that sphere is a three dimensional body so it will have three parameters x, y and z, so if we are asked to write the equation then it will be x2 + y2 +z2 =a2. Now as our topic is sphere volume for finding that we need to have good knowledge of radius of sphere, the formula for the radius of circle is given below,

V = 4/3π r3

Here π  is a constant whose  value will be 22/7 and 4/3 is also a constant , if we see here then volume of the sphere is totally depend on radius as the radius increases volume will increase and as the radius decreases  it will decrease. If we see a problem in which we are asked to calculate the volume of a sphere and radius is given as seven so we can calculate the volume as

V = 4/3πr3

V = 4/3 *22/7 *7*7

Seven will cancel out with seven and we remain with

V = 4/3 *22*49

V = 1437.33

We can also derive one more formula if we will calculate the value of 4/3π, so the value of this will be 4.19 so new formula for the volume will be 4.19 r3. We can also calculate the volume by this formula as well

For finding the cube of any number you can use cube root calculator and cube roots are important for Tamilnadu education board

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straightline

A line which is not prepared a curve is known as straight line.

As we know that the equation of straightline is generally in the form of:

Y = mx + b; or

Y = mx + c;

Where ‘m’ is the slope (gradient) of a line, slope and gradient both are same term.

And ‘b’ is the y- intercept.

Now we will see how to find the value of ‘m’ and ‘b’;

If we want to find the value of ‘b’ then we need to find where the line intersects the y- axis. Than we are find the value of ‘m’:

We know that ‘m’ is the slope of line, and then the value of ‘m’ is:

m = Change in y,

Change in x

Suppose change in ‘y’ is 5 and change in ‘x’ is 2 then we can find the value of ‘b’ and slope of a line;

We know that slope of line is:

m = Change in y,

Change in x

So put the value in the given formula:

m = 5

2

So the slope of the line is 5 and the value of b is 2.

So the equation of line by putting the value of slope and b is:

We know that the equation of line is:

Y = mx + b;

Put value of slope and y- intersect we get the equation of line.

Y = 5x + 2;

Now we will see slope of the straight line.

Suppose the coordinates of a straight line is p­1, p­2 and q­1, q­2 and ‘m’ is the slope of a line, and then we use following formula for finding the slope of a straight line.

m = q1 – q­2,

p1 – p­2

Suppose we have the values of coordinates is (3, 6) and (7, 9), then by using these coordinates find the slope of a line.

We know that the slope of a straight line is:

m = 1 – y­2,

x1 – x­2

Now put the values of these coordinates we get:

m = 6 – 9,

3 – 7

So the slope of a straight line is:

m = -3

-4

So the slope of line is 0.74.

As we know that the radius of a circle is 2πr, by using this formula we can find out the Radius of a Circle. ICSE board sample papers for class 12 are very useful for exam point of view.

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Define Slope

The perception of a slope is central to differential calculus. For non-linear functions, the small change in the rate varies along the curve. The slope or we can say its gradient of line (gradient means the points in the direction of the greatest rate with increase of the scalar field), which describe its steepness, incline or grade and the value which is higher indicates a steeper (that means having the sharp inclination), incline. It is not defined for horizontal or vertical lines.

In the slope of a line we have to follow some of the steps for finding the slope formula for the line.

Step1: – First we find the difference of both the ‘x’ and ‘y’ coordinates. And we have to place both the coordinates in the ratio.

Step 2: – After that we take two points on a line, because we are using two sets of order pair both the coordinates having values ‘x’ and ‘y’.

Step 3: – If a line has a negative slope then it goes down from left to right.

Step 4: – If a line has a positive slope then it goes up from left to right.

Step 5: – IF a line has is vertical then the slope is undefined.

The slope formula for given two points.

The two points are (p1, q1) and (p2, q2)

Then the slope of the line is denoted by ‘m’.

m = rise = change in ‘q’   =   q– q1,

run     change in ‘p’        p–  p1,

Where, the value of (p1 ≠ p2),

In case of algebra, if ‘y’ is the linear function of ‘x’, then the coefficient of ‘x’ is known as slope of the line. If the equation of the line is given by

Y = mx + c; where m is the slope of the line. The line equation is known as slope – intercept form. Now we will see what is the Distance Formula?

The two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:

⇨ d = √ (x2 – x1)2 + (y2 – y1)2. The ICSE class 12 sample papers is very useful for exam point of view.

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slope worksheet

In the previous post we have discussed about linear equations calculator and In today’s session we are going to discuss about slope worksheet, A slope describes the steepness, inclination of a line. In simple terms slope is defined as the ratio of rise when divided by the run between two points on the line. The slope worksheet help in finding the points of a line which in the plane consisting of the x and y axes which is represented by the letter ‘m’ and is defined as the change in y coordinate by the change in x coordinate between the two distinct point on the line. We can also write it as

∆y      rise

m =  —— = ——– .

∆x        run

here the symbol Ã¢ÂˆÂ† (pronounced as delta) is used which means the change or the difference.

If the two points are given suppose (x1,y1) and (x2,y2) then the change in x from one to the another will be considered i.e. x2 – x(run) whereas the change in y will be y– y(rise) now the new formula takes place will be

y– y1

m = ———-

x2 – x1

these formula will not work in the case of vertical line.

To understand this in the more precise manner we will take one example:

suppose a line runs through two points : s = (2,1) and t(13,6) now as stated in the above formula we will follow the following steps.

∆y        y– y1

m = —— = ———–

∆x        x2 – x1

6 – 2

= ——– (substitute the value in the formula)

13 – 1

= 4/12 (calculation takes place)

= 1/3

you can even find the information related to the box and whisker plots which contains the information related to its graphs and all the necessary things which is related to this. You can even visit the Indian educational portals to get the information related to the board activities such as Andhra secondary education board.

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linear equations calculator

In the previous post we have discussed about algebra calculator online and To understand about the linear equations calculator, which is the part of 7th grade math, we need to first understand how to get the solution of the linear equation. There exist a variable in the linear equation and to find the value of the given variable is called solving the linear equation.  For this we simply need to separate the constant and the variables in the given linear equation so that the value of the variable is calculated.  If we have a equation, which contains the variables and the constants on both sides of the equation, we will take the steps such that the all the terms containing the variables appears on the left side of the equation and the constants appear on the right side of the equation.

If you want to get information about cbse text books, you can Refer this,

Let us make it more clearly with the help of the following example:

2x + 6 = 8x + 4

We will try to move all the variables on the one side of the equation and the constants on the other side of the equation. For this we will first subtract 2x from both sides of the equation and get :

2x + 6 – 2x  = 8x + 4 -2x

We get :

6 = 8x – 2x + 4

6 = 6x + 4

Now we will subtract 4 from both sides of the equation to get :

6 – 4 = 6x + 4 – 4

Or  we get :

2 = 6x

Now we divide both sides of the equation by 6 and get :

2 / 6 = 6x / 6

1/3 = x

Thus we get the solution to the given equation.  If we put the value of x in the equation, lhs = rhs

In the next session we will discuss about slope worksheet and You can visit our website for getting information about online math tutor.

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