Answer :
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
[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
