Answer:
[tex]y=48[/tex]
Step-by-step explanation:
Question :
Given:
[tex]y[/tex] varies directly with [tex]x[/tex]
when [tex]x=2, y=16[/tex]
To find value of [tex]y[/tex] when [tex]x=6[/tex]
Solution:
From the given data we have:
[tex]y[/tex] ∝ [tex]x[/tex]
Thus, we have:
[tex]y=kx[/tex]
where [tex]k[/tex] is the constant of proportionality.
We can find the value of [tex]k[/tex] by plugging in the given values.
when [tex]x=2, y=16[/tex]
[tex]16=k(2)[/tex]
Dividing both sides by 2.
[tex]\frac{16}{2}=\frac{k(2)}{2}[/tex]
[tex]8=k[/tex]
∴ [tex]k=8[/tex]
So, the equation to find [tex]y[/tex] when [tex]x=6[/tex] will be:
[tex]y=8\times 6=48[/tex]
Thus, when [tex]x=6, y=48[/tex] (Answer)
