Question

Are these two problems proportional or non-proportional? Why or why not? Explain your reasoning below.

y=3/4x
y=1/2x-6

Answer 1

Given:

`y=(3)/(4)x`

`y=(1)/(2)x-6`

To find:

Whether the above functions are proportional or non-proportional?

Solution:

If y is proportional to x, then

`y\propto x`

`y=kx`

where, k is constant of proportionality.

The proportional relationships are in the form of
`y=kx` and they passes through (0,0).

Putting x=0 and y=0 in the given equations.

`y=(3)/(4)x`

`0=(3)/(4)(0)`

`0=0`

It is a true statement.

`y=(1)/(2)x-6`

`0=(1)/(2)(0)-6`

`0=0-6`

`0=-6`

It is a false statement.

Therefore,
`y=(3)/(4)x` is proportional and
`y=(1)/(2)x-6` is non-proportional.