To solve for [tex]\( y \)[/tex] when [tex]\( x = 2 \)[/tex] and given that the value of [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we can use the direct variation formula which is:
[tex]\[ y = kx \][/tex]
Here, the constant of proportionality [tex]\( k \)[/tex] is given as [tex]\( -17 \)[/tex].
Substitute the values of [tex]\( x \)[/tex] and [tex]\( k \)[/tex] into the direct variation formula:
[tex]\[ y = (-17) \cdot 2 \][/tex]
Now, perform the multiplication:
[tex]\[ y = -34 \][/tex]
Therefore, when [tex]\( x = 2 \)[/tex], the value of [tex]\( y \)[/tex] is [tex]\( -34 \)[/tex].
