Question

What is the constant of proportionality for the relationship shown in the table

A.1/2

B.2

C.4

D.8

Answer 1

Option A is correct

`(1)/(2)`

Explanation:

Direct proportionality states:

if
`y \propto x`

then, the equation is in the form of:

`y = kx` ......[1] where, k is the constant of proportionality.

As per the statement:

Consider any points from the given table:

Let (x, y) = (4, 2)

Substitute these points in [1] we have;

`2 = 4k`

Divide both sides by 4 we have;

`(1)/(2) = k`

or

`k=(1)/(2)`

Therefore, the constant of proportionality for the relationship is,
`(1)/(2)`

Answer 2

Option A

`1/2`

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

For
`x=2, y=1`

`k=y/x=1/2`

For
`x=4, y=2`

`k=2/4=1/2`

For
`x=6, y=3`

`k=3/6=1/2`

For
`x=8, y=4`

`k=4/8=1/2`