Question

If the values in the table below model a proportional relationship, what is the equation for the function?

Answer 1

Given:

The table represents a proportional relationship.

To find:

The equation of the function.

Solution:

If y is directly proportional to x, then

$y\propto x$

$y=kx$     ...(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

$1=k(2)$

$\dfrac{1}{2}=k$

Putting $k=\dfrac{1}{2}$, we get

$y=\dfrac{1}{2}x$

Therefore, the correct option is A.