**Step1: –** To find the value of slope first it is necessary to find the difference of both the ‘x’ and ‘y’ coordinates. And also put both the coordinates in the ratio or in (p / q form).

**Step 2: –** After then mark two points on a line, because here we are using two sets of order pair.

**Step 3: –**There are two exception case for the slope of a line if a line has a negative slope then it moves from left to right and in case of positive slope it moves from right to left. In the case if a line is vertical then the slope of a line is indistinct.

(know more about slope intercept , here)

The slope formula for given two points. The two points are (p_{1,} q_{1}) and (p_{2}, q_{2}), then the slope of the line is denoted by ‘m’.

m = rise / run = change in ‘q’/ change in ‘p’ = q_{2 }– q_{1 }/ p_{2 }– p_{1}. here, the value of (p_{1} ≠ p_{2}).

If we talk about the slope in algebra, if ‘q’ is the linear function of ‘p’, then the coefficient of ‘p’ is called as slope of the line. The equation of line is given as:

q = mp + c; here ‘m’ denotes the slope of the line and ‘q’ is intersept form.

Now we will talk about what is the Distance Formula?

The two points (p_{1}, q_{1}) and (p_{2}, q_{2}), then distance find between these points is given by the formula:

Ã¢ÂÂ¨ d = √ (p_{2} – p_{1})^{2} + (q_{2} – q_{1})^{2}. Now we will talk about **System of Linear Equations**. It means two or more linear equations. Before entering in the examination hall please go through cbse sample papers.

]]>

m = a1 – a2 / a1– a2, here‘m’ is the slope of line and a1, a2 are the points on y- axis and b1, b2 are the points on x- axis. The above equation can also be described as:

=> m = a2– a1 / b2 – b1,

The gradient of a line can be represented by following formula:

=> m = tan θ, Now understand slope of a line with help of an example:

Suppose that a line follows two points: S = (4, 4) and T = (8, 6), therefore by the division of the change in y – coordinate by the change in x – axis, one can easily calculate the slope of the line. The formula for finding the slope of a line is:

=> m = a2– a1 / b2 – b1,

= 8 – 4 / 6 – 4,

= 4 / 2;

= 2; This is how we Define slope of a line. If the slope of a line is equal to -1, then two lines are perpendicular to each other. This is all about Slope Worksheets. (know more about Slope Worksheets, here)

In nature **Surface Waves** can be electromagnetic which is used to propagate the interface. To get more information about surface wave then see the **cbse syllabus for class 9th**.

]]>

x – x_{1} = m (y – y_{1}),

If the value of x_{1} is 1 and value of y_{1} is 2 and value of slope m is 2 then the equation of line will be,

x – 1 = 2 (y -2),

x – 2y = -3. (know more about Point Slope, here)

This is the required equation of line, we can also find the slope of line if we know that from which two point the line is passing, suppose a line is passing through points (x_{1} ,y_{1}) and (x_{2} ,y_{2}) then the slope of the line will be,

m = y_{2} –y_{1} / x_{2} –x_{1,}

If we have one point as (1,0) and other as (2 ,1) then the slope of the line will be,

m = (1 – 0) / (2 -1),

m = 1.

So, the value of slope will be one, we can also write the equation of line as,

x – x_{1} = (y_{2} –y_{1} / x_{2} –x_{1}) (y –y_{1}),

In **cbse geography syllabus** topic **What is a Line Segment** is very important topic in geometry.

]]>

If we are given the two linear equations to represent the two lines and we need to find the point of intersection of the two lines, we mean that we need to find the solution for the intersection of the two lines. It can be done algebraically as well as by the graphical representation. By the method of graphical representation, we will draw the graph of the two lines on the graph paper by simply plotting the points and then we will observe the point which is common for both the equations. The coordinates which are common for both the equations is called the point of intersection of the two equations. (know more about Line , here)

In case we observe that the two given lines do not have any point of intersection, then we simply conclude that the two lines are parallel. In case the two lines have more than one intersecting point, then we observe that the lines have infinite points of intersection and thus we say that the two lines are overlapping. We can also say that the two equations are representing the same lines. While **Finding The Area Of A Triangle**, we can take the help of online math tutor, which can guide and support you any time free of cost. What all we need is the computer and the internet connection. To learn more about the area of the triangle, we can take the help of **Central Board Of Secondary Education Books**, which has ample of examples and exercised on each and every topic.

]]>

When we talk about the quadratic equation ,in this variable have the exponent value equal to 2, that is define as a x 2 + x + c = 0.

So for solving the equation we explain some of the rules that are define below:

whenever solve an equation first of all define the type of equation . After it shift all the constant values at one side and all the variables at one side. At the time of shifting values their sign are changed means plus sign changed into the negative sign and vice versa.(want to Learn more about Equations, click here),

We can explain it by an example as if there is an equation 2 a – 6 = 3 – a, shift the constant at one side and variables at one side as 2 a + a = 3 + 6

3 a = 9

a = 9 / 3 = 3.

**How to simplify expressions** have different ways of solving the complex expressions into the more understandable form that helps students in solving these problems.

**Previous years cbse board question papers** provide to the students by the cbse board that support them to identify the pattern of question papers in the exam and help them in securing the good marks.

]]>

It is very much used in the mathematics for various calculations as change in the position of the object with respect to the time is defined as the velocity.

**Derivative of sin** is defined as d sin (s) / d s. In this expression differentiation of the sin function define with respect to x that is equal to cos (s).

It is defined through some steps:

d / d s (sin (s)) = lim h → 0 sin (s+ h) – sin (s) / h,

= lim h → 0 sin (s) cos (h) + cos (s) sin (h) – sin (h) / h ,

= cos (s) [sin (h) / h ] – sin (s) [ 1 – cos (h) / h],

So, d / d s (sin (s)) = cos (s) (1) – sin (s) (0),

= d / d s (sin (s)) = cos (s).

As we prove that the derivative of sin function is equal to the cos function and when we find the derivative of the cos function it is equal to the sin function means derivative of sin and cos function are cos and sin function respectively.

**Formula for Volume of a Sphere** is define as the volume of the three dimensional space that is describe as the volume of the ball and it can be expressed as V = 4 / 3 π r³.**cbse physics syllabus **defines all the related topics of the physics session by session that is provided by the central board of secondary education.

]]>

m = y2 – y1 / x2 – x1 that means slope of the line is expressed as the ratio of change in the coordinate of y axis to the change in the coordinate of x axis. ( if the value of x1 and x2 are equal then it will not represent the line).

It is also define in terms of angle that is created between the line and the x axis. So the tangent of the angle is defining the slope of the line. If the created angle between the line and the x axis is Ã¢ÂÂthen the slope of that line is expressed as m = tan Ã¢ÂÂ.

As example if the angle is of 45’then find the slope of the line is calculated as

m = tan 45’

m = 1. (So the value of the slope is for the line is 1).

**Pythagorean Theorem worksheet** has the several examples to understand the Pythagorean Theorem.

**CBSE math syllabus** provided by the CBSE boards describe all the topics of maths for students of the class they are belongs.

]]>

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 (x_{1}, y_{1}) and (x_{2}, y_{2}) and we are asked to find the equation of the line then we can find the equation of line as

y – y_{1}= m (x – x_{1})

Here the value of m will be = y_{2} – y_{1} /x_{2} – x_{1}

So we can rewrite our line equation as

y – y_{1} = (y_{2} – y_{1} /x_{2} – x_{1}) * (x –x_{1})

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 = y_{2} – y_{1} /x_{2} – x_{1}

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

]]>

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**.

]]>

V = 4/3π r^{3}

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 = 4/3πr^{3}

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 r^{3}. 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**

]]>