Question

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

Answer 1

Given:

$y=\dfrac{3}{4}x$

$y=\dfrac{1}{2}x-6$

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.

$y=\dfrac{3}{4}x$

$0=\dfrac{3}{4}(0)$

$0=0$

It is a true statement.

$y=\dfrac{1}{2}x-6$

$0=\dfrac{1}{2}(0)-6$

$0=0-6$

$0=-6$

It is a false statement.

Therefore, $y=\dfrac{3}{4}x$ is proportional and $y=\dfrac{1}{2}x-6$ is non-proportional.