Given:
The table represents a proportional relationship.
To find:
The equation of the function.
Solution:
If y is directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
where, k is the constant of proportionality.
From the given table it is clear that the function passes through (2,1). So, the equation must be satisfied by the point (2,1).
Putting x=2 and y=1 in (i), we get
[tex]1=k(2)[/tex]
[tex]\dfrac{1}{2}=k[/tex]
Putting [tex]k=\dfrac{1}{2}[/tex], we get
[tex]y=\dfrac{1}{2}x[/tex]
Therefore, the correct option is A.
