Given:
y is proportional to x.
y=10 and x=8.
To find:
The constant of proportionality and the equation for the proportional relationship.
Solution:
y is proportional to x.
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
Putting y=10 and x=8, we get
[tex]10=k(8)[/tex]
[tex]\dfrac{10}{8}=k[/tex]
[tex]\dfrac{5}{4}=k[/tex]
Putting [tex]k=\dfrac{5}{4}[/tex] in (i), we get
[tex]y=\dfrac{5}{4}x[/tex]
Therefore, the contestant of proportionality is [tex]k=\dfrac{5}{4}[/tex] and the equation for the proportional relationship is [tex]y=\dfrac{5}{4}x[/tex].