# Slope Formulas

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```					                                Slope Formulas
Slope Formulas

There are a few concepts that come along with the slope concept like intercept form and point
slope formula. Again the concept intercept form includes x and y intercept. Finding slope is
done with the help of the point slope formula. Thus all these topics are interrelated.

Formula for Slope of a Line

The slope of a line means the steepness or incline of the line. The higher the slope value the
more is the steeper incline.The slope of a line including the x axis and y axis is represented by
m and is defined as the change in the y coordinate divided by the corresponding change in the
x coordinate, between two distinct points on the line.

The slope formula of the line is : Slope (m) = [ (y2 - y1)/(x2 - x1)]

Slope (m) = RiseRun (Rise = change in the y co-ordinate; Run = change in the x co-ordinate)

In the above given graph, the Rise is given for the points B (4,2) and C (4,4) and the Run is
given for the points A (2,2) and B (4,2)

Rise = change in the y - coordinate = 4-2 =2
Know More About What is a Equilateral Triangle

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Run = change in the x- coordinate = 4-2 =2

Using the slope formula, we get :

Slope( m ) = RiseRun = 22 =1

How to Find the Slope of a Line

Determine the slope of a line, which contains the points A (-1, -2), B (-2, 1):

Solution : Here, x1 = -1, x2 = -2, y1 = -2, y2 = 1.

Slope of the line, m = [ (y2−y1)(x2−x1)]

= [(1+2)(−2+1)], = [3(−1)], Slope of the line (m) = -3

Finding Slope Examples

Here are few other slope formula examples worked out for you with explanations

Problem 1 : Find the slope of the equation y=4x-3

Solution : Y = 4x - 3

It is in the slope form y = mx + b.   So, slope(m) = 4

Problem 2 : Find the slope of the equation 3y = 6x - 12

Solution : 3y = 6x – 12     Divide by 3 on both sides,

Y = 2x – 4 So, slope(m) = 2

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Total Surface Area of a Cylinder
Total Surface Area of a Cylinder

A Cylinder has a circular base. It can be of the shape of a pillar, a rubber tube, the trunk of a
tree, etc. The term 'circular cylinder' is commonly used to describe aright circular cylinder. A
right circular cylinder is a circular cylinder that has perpendicular base and height. The
diagram shown below is of a right circular cylinder.

In the above diagram, h = height of the circular cylinder, r = radius of base of circular cylinder

We can also say that a circular cylinder is a rolled form ofa rectangle.The area of the rectangle
that forms a cylinder is called the curvedsurface area of a cylinder, since the rectangle forms
the curved surface of the cylinder.

When we cut a cylinder vertically, thecross section obtained is a rectangle. In other words,
when a rectangle is revolved around one of its sides, a cylinder is obtained.

When we add the area of the top and bottom circles of a cylinder to its curved surface area,
we get theTotal surface area of a cylinder.

Curved Surface Area of a Cylinder

The curced surface area of a cylinder is given by the following formula,

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Curved Surface Area = 2 * π * r * h, where, π = 22/7 or 3.14

r = radius of the base circles of cylinder, h = height of the cylinder

Total Surface Area of a Cylinder

Total Surface Area = (π * r²) + (π * r²) + (2 * π * r * h),

where (π * r²) = Area of the base circle, (2 * π * r * h) = Area of the curved surface of cylinder

Solved Examples on Cylinders

Given below are some of the examples on Cylinder

Example 1: Find the curved surface area of the cylinder with height = 15 cm and radius of
base circle = 5 cm.

Solution : Given, Radius, r = 5 cm, Height, h = 15 cm

Area of curved surface, CSA = 2 * π * r * h

= 2 * 3.14 * 5 x 15

= 471 cm²

Example 2: Find the Total Surface Area of a cylinder whose height is 20 meters and radius of
base circle is 2 meters.

Solution : Given,

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