Which does not show a direct variation between \( x \) and \( y \)?
A. \( y = \frac{x}{9} \)
B. \( y = 2x \)
C. \( y = 0.5x \)
D. \( y = \frac{9}{x} \)
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If \( f(x) \) varies directly with \( x \), and \( f(x) = 8 \) when \( x = 6 \), write the direct linear variation equation.
A. \( f(x) = \frac{3}{4}x \)
B. \( f(x) = 6x \)
C. \( f(x) = 8x \)
D. \( f(x) = \frac{4}{3}x \)
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Find the constant of variation for the relationship \( f(x) = 30x \).
A. 10
B. 30
C. \( x \)
D. \( f(x) \)
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If \( f(x) \) varies directly with \( x \), and \( f(x) = 56 \) when \( x = 8 \), find the value of \( f(x) \) when \( x = 2 \).
A. 4
B. 7
C. 8
D. 14
Answer (2)
( 1 ) d i rec t v a r ia t i o n b e tw ee n x an d y : y = k ⋅ x an d k ∈ R A n s . NOT d i rec t i s D ( 2 ) f ( x ) = m ⋅ x an d f ( 6 ) = 8 ⇒ m ⋅ 6 = 8 ⇒ m = 6 8 = 3 4 ⇒ A n s . D ( 3 ) f ( x ) = 30 x ⇔ x f ( x ) = 30 ⇒ co n s t an s = 30 A n s . B .
( 4 ) f ( x ) = m ⋅ x an d f ( 8 ) = 56 m ⋅ 8 = 56 ⇔ m = 8 56 = 7 ⇒ f ( x ) = 7 x ⇒ f ( 2 ) = 7 ⋅ 2 = 14 A n s . D .
The equation that does not show direct variation is D. The direct variation equation based on the given points is D. The constant of variation for the function is B, and when calculated for x = 2 , the value of f ( x ) is D, which is 14.
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