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Entry Task – SHOW WORK

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2.2 Direct Variation Target: I can Write and interpret direct variation equations

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Definition: Y varies directly as x means that y = kx where k is the constant of variation. Another way of writing this is k = In other words: * the constant of variation (k) in a direct variation is the constant (unchanged) ratio of two variable quantities.

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When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.

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Direct Variation Direct variation uses the following formula:

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Direct Variation example: if y varies directly as x and y = 10 as x =2.4, find x when y =15. what x and y go together?

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Direct Variation If y varies directly as x and y = 10 find x when y =15. y = 10, x = 2.4 make these y 1 and x 1 y = 15, and x = ? make these y 2 and x 2

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Direct Variation if y varies directly as x and y = 10 as x = 2.4, find x when y =15

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Direct Variation How do we solve this? Cross multiply and set equal.

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Direct Variation We get: 10x = 36 Solve for x by diving both sides by 10. We get x = 3.6

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Direct Variation Lets do another. If y varies directly with x and y = 12 when x = 2, find y when x = 8. Set up your equation.

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Direct Variation If y varies directly with x and y = 12 when x = 2, find y when x = 8.

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Direct Variation Cross multiply: 96 = 2y Solve for y. 48 = y.

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Note: X decreases, 10, 5, 3 And Y decreases. 30, 15, 9 What is the constant of variation of the table above? Since y = kx we can say Therefore: 30/10=k or k = 315/5=k or k = 3 9/3=k or k =3Note k stays constant. y = 3x is the equation! Examples of Direct Variation:

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Find the value of k. y=kx Direct variation formula 42 = k(7)Replace y with 15 and x with 5. 42= k(7) 7 7Divide each side by 5 6 = kSimplify Equation? y = 6x Y varies directly as x. Find the constant of variation and write an equation for the direct variation when y = 42 when x = 7

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Tell if the following graph is a Direct Variation or not. No Yes No

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Yes No Tell if the following graph is a Direct Variation or not

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Given that y varies directly with x, and y = 6 when x=-5, Find y when x = -8. HOW??? 2 step process 1. Find the constant variation. k = y/x or k = 6/-5 = -1.2 k = Use y = kx. Find the unknown (x). y= -1.2(-8) x= 9.6 Therefore: X =-8 when Y=9.6 Using Direct Variation to find unknowns (y = kx)

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Using Direct Variation to solve word problems Problem: A car uses 8 gallons of gasoline to travel 290 miles. How much gasoline will the car use to travel 400 miles? Step One: Find points in table Step Two: Find the constant variation and equation: k = y/x or k = 290/8 or y = x Step Three: Use the equation to find the unknown. 400 =36.25x or x = 11.03

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Homework P. 71 # 7-47 odds Challenge - # 54

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