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 Learn More Height of an Equilateral Triangle Tutorvista.com
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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, Tutorvista.com
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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, Radius, r = 2 m Height, h = 20 m
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Thank You
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