Answered

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If [tex][tex]$y$[/tex][/tex] varies directly as [tex][tex]$x$[/tex][/tex], and [tex][tex]$y$[/tex][/tex] is 20 when [tex][tex]$x$[/tex][/tex] is 4, what is the constant of variation for this relation?

A. [tex]\frac{1}{5}[/tex]
B. [tex]\frac{4}{5}[/tex]
C. 5
D. 16

Sagot :

GinnyAnswer
To find the constant of variation when [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], we use the direct variation formula:

[tex]\[ y = kx \][/tex]

where [tex]\( k \)[/tex] is the constant of variation. Given that [tex]\( y = 20 \)[/tex] when [tex]\( x = 4 \)[/tex], we substitute these values into the equation:

[tex]\[ 20 = k \cdot 4 \][/tex]

To solve for [tex]\( k \)[/tex], we divide both sides of the equation by 4:

[tex]\[ k = \frac{20}{4} \][/tex]

[tex]\[ k = 5 \][/tex]

Therefore, the constant of variation is:

5

So, the correct answer is:

5
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