Sure! Let's solve for [tex]\( y \)[/tex] given that the value of [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex].
The direct variation relationship means we have the equation:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
Given:
[tex]\[ x = 12 \][/tex]
[tex]\[ k = -4 \][/tex]
We can substitute these values into the equation:
[tex]\[ y = kx \][/tex]
[tex]\[ y = (-4) \times 12 \][/tex]
Now, we solve for [tex]\( y \)[/tex]:
[tex]\[ y = -4 \times 12 = -48 \][/tex]
Therefore, when [tex]\( x = 12 \)[/tex] and [tex]\( k = -4 \)[/tex], the value of [tex]\( y \)[/tex] is:
[tex]\[ y = -48 \][/tex]
