Direct Variation: Direct Variation Algebra
Review: 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 times
Direct 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 x
Direct 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 = - 0.75
Direct 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 = 0.5
Watch 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 notes
Further 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!!