2 Write and interpret direct variation equations Target: I canWrite and interpret direct variation equations
3 Another way of writing this is k = 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.
4 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.
6 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?
7 Direct VariationIf y varies directly as x and y = 10 find x when y =15.y = 10, x = make these y1 and x1y = 15, and x = ? make these y2 and x2
8 Direct Variationif y varies directly as x and y = 10 as x = 2.4, find x when y =15
9 How do we solve this? Cross multiply and set equal. Direct VariationHow do we solve this? Cross multiply and set equal.
10 Direct Variation We get: 10x = 36 Solve for x by diving both sides by 10.We get x = 3.6
11 Direct Variation Let’s do another. If y varies directly with x and y = 12 when x = 2, find y when x = 8.Set up your equation.
12 If y varies directly with x and y = 12 when x = 2, find y when x = 8. Direct VariationIf y varies directly with x and y = 12 when x = 2, find y when x = 8.
13 Cross multiply: 96 = 2y Solve for y. 48 = y. Direct VariationCross multiply: 96 = 2ySolve for y = y.
14 Examples of Direct Variation: Note: X decreases,10, 5, 3And Y decreases.30, 15, 9What is the constant of variation of the table above?Since y = kx we can say Therefore:30/10=k or k = 3 15/5=k or k = 39/3=k or k =3 Note k stays constant.y = 3x is the equation!
15 Y varies directly as x. Find the constant of variation and write an equation for the direct variation when y = 42 when x = 7Find the value of k.y=kx Direct variation formula42 = k(7) Replace y with 15 and x with 5.42= k(7)Divide each side by 56 = k SimplifyEquation?y = 6x
16 Tell if the following graph is a Direct Variation or not. YesNoNoNo
17 Tell if the following graph is a Direct Variation or not. 1.2.YesNo3.4.NoYes
18 Using Direct Variation to find unknowns (y = kx) Given that y varies directly with x, and y = 6 when x=-5,Find y when x = HOW???2 step process1. Find the constant variation.k = y/x or k = 6/-5 = -1.2k = -1.22. Use y = kx. Find the unknown (x).y= -1.2(-8)x= 9.6Therefore:X =-8 when Y=9.6
19 Using Direct Variation to solve word problems 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 tableStep Three: Use the equationto find the unknown.400 =36.25xor x = 11.03Step Two: Find the constant variation and equation:k = y/x or k = 290/8 or 36.25y = x