2-3 direct variations. direct variation: y = kx y varies directly with x y varies directly as x k =...
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2-3 Direct Variations
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Direct Variation: y = kx
• y varies directly with x
• y varies directly as x
• k = constant of variation = slope
• The graph of a direct variation ALWAYS goes through (0,0), the origin
• K is never 0.
• K can be positive or negative.
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Direct Variation or not? Direct Variation or not?
Solve for ySolve for y Put the equation in the form y = kx Put the equation in the form y = kx Does y vary directly with x? If so, find k.Does y vary directly with x? If so, find k.
1.1. 2x – 3y = 12x – 3y = 1
2.2. 2x – 3y = 0 2x – 3y = 0
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3. ½ x + 1/3y = 0
4. 7y = 2x
5. 3y + 4x = 8
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Write and solve a direct variation
• Use the given x and y values to find k.
• Rewrite your equation with the value for k and the x and y variables.
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• Suppose y varies directly as x, and y = 9 when x = -3.
• Use the direct variation equation to find x when y = 15.
Write a Direct Variation Equation
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If y = 2 2/3 when x = ¼ ,find y when
x= 11/8
If y =4 when x =12, find y when x = -24
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Data Tables
• y = kx also equals y/x = k
• If k (constant of variation) is the same for each y divided by x, then you have a direct variation.
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Determine if each data table represents a direct variation. If so,
write the equation.
X Y
-2 3.2
1 2.4
4 1.6
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X Y
4 6
8 12
10 15
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XX YY
-2-2 11
22 -1-1
44 -2-2
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X Y
-1 2
1 2
2 -4
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Write the direct variation equation that goes through each point.
• Use (x,y) in y=kx.
• Find k, write your equation.
• 1) (1,2)
• 2) ( -3, 14)