Question

Does this graph represent direct proportionality?

• A. Yes
• B. No

Answer 1

The correct option is B No

A graph of direct variation always passes through the origin. This is not true for the given graph, thus this cannot represent direct proportionality.

Also, we know, for direct proportionality,

$\frac{y}{x}=k$, where $k$ is the constant of proportionality.

If we take values of $x$ and $y$ from the given figure, to determine $k$, we see that:

For $y=3$ and $x=6$,

$k=\frac{3}{6}=0.5$

And, for $y=8$ and $x=9$,

$k=\frac{8}{9}=0.89$

Since the value of $k$ is not constant, we cannot call this graph a representation of direct variation.

Option (b.) is correct. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->