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:
[tex]k = \frac{y}{x}[/tex]
Where k is the constant of proportionality.
In table (A)
x = 2, y = 4
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{4}{2}[/tex]
[tex]k = 2[/tex]
x = 4, y = 9
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{9}{4}[/tex]
[tex]k = 2.25[/tex]
Both values of k are different. Hence, no proportional relationship
In table (B)
x = 3, y = 4
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{4}{3}[/tex]
[tex]k = 1.33[/tex]
x = 9, y = 16
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{16}{9}[/tex]
[tex]k = 1.78[/tex]
Both values of k are different. Hence, no proportional relationship
In table (C):
x = 4, y = 12
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{12}{4}[/tex]
[tex]k = 3[/tex]
x = 5, y = 15
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{15}{5}[/tex]
[tex]k = 3[/tex]
x = 6, y = 18
[tex]k = \frac{y}{x}[/tex]
[tex]k = \frac{18}{6}[/tex]
[tex]k = 3[/tex]
This shows a proportional relationship because all values of k are the same for this table
