Direct Variation What is it and how do

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Direct Variation What is it and how do I know when I see it?

Direct Variation What is it and how do I know when I see it?

Definition: y varies directly as x means that y = kx where k is

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.

Examples of Direct Variation: Note: x increases, 6, 7, 8 And y increases. 12,

Examples of Direct Variation: Note: x increases, 6, 7, 8 And y increases. 12, 14, 16 What is the constant of variation of the table above? Since y = kx we can say Therefore: 12/6=k or k = 2 14/7=k or k = 2 16/8=k or k =2 Note k stays constant. y = 2 x is the equation!

Examples of Direct Variation: Note: x decreases, 10, 5, 3 And y decreases. 30,

Examples of Direct Variation: 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 = 3 15/5=k or k = 3 9/3=k or k =3 Note k stays constant. y = 3 x is the equation!

Examples of Direct Variation: Note: x decreases 9, 4, 2 And y decreases. 45,

Examples of Direct Variation: Note: x decreases 9, 4, 2 And y decreases. 45, 20, 10 What is the constant of variation of the table above? Since y = kx we can say 45/9=k or k = 5 50/4=k or k = 5 Therefore: 10/2=k or k = 5 Note k stays constant. y = 5 x is the equation!

What is the constant of variation for the following direct variation? 1. 2. 3.

What is the constant of variation for the following direct variation? 1. 2. 3. 4. 4 2 ½ ¼ Answer Now

What is the constant of variation for the following direct variation? 1. 2. 3.

What is the constant of variation for the following direct variation? 1. 2. 3. 4. 4 2 ½ ¼ Answer Now

What is the constant of variation for the following direct variation? 1. 2. 3.

What is the constant of variation for the following direct variation? 1. 2. 3. 4. 3 2 1/3 ½ Answer Now

What is the constant of variation for the following direct variation? 1. 2. 3.

What is the constant of variation for the following direct variation? 1. 2. 3. 4. 2 5 10 ½ Answer Now

Is this a direct variation? If yes, give the constant of variation (k) and

Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 12/4 or 3 Equation? y = 3 x

Is this a direct variation? If yes, give the constant of variation (k) and

Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 4/12 or 1/3 Equation? y = 1/3 x

Is this a direct variation? If yes, give the constant of variation (k) and

Is this a direct variation? If yes, give the constant of variation (k) and the equation. No! The k values are different!

Is this a direct variation? If yes, give the constant of variation (k) and

Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 2/12 or 1/6 Equation? y = 1/6 x

Is this a direct variation? If yes, give the constant of variation (k) and

Is this a direct variation? If yes, give the constant of variation (k) and the equation. Yes! k = 6/4 or 3/2 or 1. 5 Equation? y = 1. 5 x

Is this a direct variation? If yes, give the constant of variation (k) and

Is this a direct variation? If yes, give the constant of variation (k) and the equation. No! The k values are different!

Which is the equation that describes the following table of values? 1. 2. 3.

Which is the equation that describes the following table of values? 1. 2. 3. 4. y = 5 x y = 2 x y= ½x xy = 200 Answer Now

Which is the equation that describes the following table of values? 1. 2. 3.

Which is the equation that describes the following table of values? 1. 2. 3. 4. y y = = 1. 5 x 2 x 2. 5 x 20 x Answer Now

Which is the equation that describes the following table of values? 1. 2. 3.

Which is the equation that describes the following table of values? 1. 2. 3. 4. y y = = 4 x 2 x ½x ¼x Answer Now

Which is the equation that describes the following table of values? 1. 2. 3.

Which is the equation that describes the following table of values? 1. 2. 3. 4. y = 6 x y = 4 x y= ½x xy = 2 x Answer Now

Definition: y varies directly as x means that y = kx where k is

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.