Question

Which of the following shows a proportional relationship between x and y?

J

x	y
2	$\frac{1}{8}$
4	$\frac{1}{4}$

K

x	y
$\frac{5}{2}$	5
5	10

J

x	y
2	$\frac{1}{2}$
8	$\frac{1}{4}$

• A. K
• B. K and L
  
• C. J
• D. J and K
  

Answer 1

The correct option is D J and K


Table J

x	y	$\frac{x}{y}$
2	$\frac{1}{8}$	$2÷\frac{1}{8}$ $=\frac{2}{1}\times \frac{8}{1}$ $=16$
4	$\frac{1}{4}$	$4÷\frac{1}{4}$ $=\frac{4}{1}\times \frac{4}{1}$ $=16$
Constant of proportionality, $k=16$ Thus, it is a proportional relationship.

Table K

x	y	$\frac{x}{y}$
$\frac{5}{2}$	$5$	$\frac{5}{2}÷5$ $=\frac{5}{2}\times \frac{1}{5}$ $=\frac{1}{2}$
5	$10$	$5÷10$ $=\frac{5}{10}$ $=\frac{1}{2}$
Constant of proportionality, $k=\frac{1}{2}$ Thus, it is a proportional relationship.

In table L

x	y	$\frac{x}{y}$
12	$\frac{1}{2}$	$12÷\frac{1}{2}=12\times \frac{2}{1}=24$
8	$\frac{1}{4}$	$8÷\frac{1}{4}=8\times \frac{4}{1}=32$

Since $\frac{x}{y}$ is not constant, x and y are not in proportion.
From the given tables, the ratio of x and y is constant only in tables J and K.