Question

Which of the following graph indicates the proportional relationship: y = 22x

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\text{The relatioship given is}y=22x$

First graph is:


Let's create the input-output relation in the form of table as:

x	10	20	30	40
y	100	200	300	400

$\text{Given equation is}y=22x$
$\text{This can be written as:}\frac{y}{x}=22$

From the table, we observe:
$\frac{\text{y}}{\text{x}}=\frac{100}{10}=\frac{200}{20}=\frac{300}{30}=\frac{400}{40}=10$

$\therefore \text{It is not the required graph}$

Second graph is:


Let's create the input-output relation in the form of table as:

x	5	10	15	20
y	110	220	330	440

$\text{Given equation is}y=22x$
$\text{This can be written as:}\frac{y}{x}=22$

From the table, we observe:
$\frac{\text{y}}{\text{x}}=\frac{110}{5}=\frac{220}{10}=\frac{330}{15}=\frac{440}{20}=22$

$\therefore \text{It is the required graph}$


Third graph is:


Let's create the input-output relation in the form of table as:

x	5	10	15	20	25
y	100	200	300	400	500

$\text{Given equation is}y=22x$
$\text{This can be written as:}\frac{y}{x}=22$

From the table, we observe:
$\frac{\text{y}}{\text{x}}=\frac{100}{5}=\frac{200}{10}=\frac{300}{15}=\frac{400}{20}=\frac{500}{25}=20$

$\therefore \text{It is not the required graph}$

Fourth graph is:


Let's create the input-output relation in the form of table as:

x	5	10	15
y	150	300	450

$\text{Given equation is}y=22x$
$\text{This can be written as:}\frac{y}{x}=22$

From the table, we observe:
$\frac{\text{y}}{\text{x}}=\frac{150}{5}=\frac{300}{10}=\frac{450}{15}=30$

$\therefore \text{It is not the required graph}$

$\text{So, only the second graph has the equation}$
$y=22x$