Question

Which table shows a proportional relationship between x and y ?

Answer 1

Answer:

Table C

Step-by-step explanation:

Given

Table A to D

Required

Which shows a proportional relationship

To do this, we make use of:

$k = \frac{y}{x}$

Where k is the constant of proportionality.

In table (A)

x = 2, y = 4

$k = \frac{y}{x}$

$k = \frac{4}{2}$

$k = 2$

x = 4, y = 9

$k = \frac{y}{x}$

$k = \frac{9}{4}$

$k = 2.25$

Both values of k are different. Hence, no proportional relationship

In table (B)

x = 3, y = 4

$k = \frac{y}{x}$

$k = \frac{4}{3}$

$k = 1.33$

x = 9, y = 16

$k = \frac{y}{x}$

$k = \frac{16}{9}$

$k = 1.78$

Both values of k are different. Hence, no proportional relationship

In table (C):

x = 4, y = 12

$k = \frac{y}{x}$

$k = \frac{12}{4}$

$k = 3$

x = 5, y = 15

$k = \frac{y}{x}$

$k = \frac{15}{5}$

$k = 3$

x = 6, y = 18

$k = \frac{y}{x}$

$k = \frac{18}{6}$

$k = 3$

This shows a proportional relationship because all values of k are the same for this table