logging in or signing up Direct Variation Scanson Download Post to : URL : Related Presentations : Let's Connect Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Copy embed code: Embed: Flash iPad Dynamic Copy Does not support media & animations Automatically changes to Flash or non-Flash embed WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 121 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: January 22, 2013 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Direct Variation: Direct Variation AlgebraReview: Review A function is a relationship that assigns exactly one output value (range) for each input value (domain). For each input there is only one corresponding output. 3 ways to view a function: Function rule Function table Graph REMEMBER: x = input = domain = independent y = output = range = dependent = also called f (x) at timesDirect Variation: Direct Variation Direct variation is a function in the form y = k (x) where k does not equal zero. k is the coefficient of x – called the constant of variation x & y vary directly with one another. In y = k (x) If x=0 then y=0, therefore… The graph of a direct variation must pass through point (0,0)Direct Variation: Direct Variation Is an equation a direct variation? If the equation can be written in the form y =k (x) where k does not equal zero then it is a direct variation. Ex. 5x + 2y = 0 -5x -5x subtract 5x from both sides 2y = -5x 2 2 divide both sides by 2 y = (-5/2)x The equation can be written as y = k x and the constant of variation is -5/2.Direct Variation: Direct Variation Is the equation a direct variation? 5x + 2y = 9 -5x -5x subtract 5x from both sides 2y = 9 – 5x 2 2 divide both sides by 2 y = 9/2 – 5/2x That is not in the form y = k (x) so it is not a direct variation.Direct Variation: Direct Variation To w rite an equation of direct variation when given a point ( x,y ) Plug in the x and y values Solve for k Ex. (4, -3) y = k (x) -3 = k (4) 4 4 -3/4 = k Plug it back into the equation y = -3/4 xDirect Variation: Direct Variation Y = k (x) can be written as y =k x Use the ratio y to tell whether y varies directly with x. x If it does, all y/x will be the same. Since y/x equals -0.75 every time, it is the constant (k). Therefore, it is a direct variation and can be written as y= -0.75 x x y y/x -3 2.25 -0.75 1 -0.75 -0.75 4 -3 -0.75 6 -4.5 -0.75 2.25/ -3 = - 0.75 -0.75/ 1 = - 0.75 -3 /4 = - 0.75 -4.5/ 6 = - 0.75Direct Variation: Direct Variation Y = k (x) can be written as y =k x Use the ratio y to tell whether y varies directly with x. x If it does, all y/x will be the same. Since y/x does not equal the same thing every time, it is not a direct variation. x y y/x 2 -1 -0.5 4 1 0.25 -6 3 -0.5 9 4.5 0.5 -1/ 2 = - 0.5 1/4 = 0.25 3 / -6 = - 0.5 4.5/ 9 = 0.5Watch the videos linked below: Watch the videos linked below Click on the links below to see further discussion: http://www.khanacademy.org/math/algebra/algebra-functions/direct_inverse_variation/v/direct-variation- 1 http://www.khanacademy.org/math/algebra/algebra-functions/direct_inverse_variation/v/direct-variation- application Please copy the examples given in the videos into your notesFurther Reference: Further Reference For more information or examples on this topic, please see: Textbook p. 277 - 283 http://www.sparknotes.com/math/algebra1/variation/section1. rhtml http://www.freemathhelp.com/direct- variation.html http://www.youtube.com/watch?v= o31s1daJaWw Please write down any specific questions you have so we can discuss them in class!! You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.