Answer:
Table 3
X. 1,3,4,5
Y. 50,150,200,250
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
Verify each table
Find the value of k for each ordered pair
If the value of k is the same for all ordered pairs, then the table represents a proportional relationship.
If the k-value is different for any of the ordered pairs, then the table does not represent a proportional relationship
Table 1
For x=2, y=6 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{6}{2}=3[/tex]
For x=4, y=12 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{12}{4}=3[/tex]
For x=5, y=18 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{18}{5}=3.6[/tex]
The values of k are different
therefore
The table 1 not represent a proportional relationship
Table 2
For x=3, y=1.5 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{1.5}{3}=0.5[/tex]
For x=5, y=2.5 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{2.5}{5}=0.5[/tex]
For x=7, y=3 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{3}{7}=0.4[/tex]
The values of k are different
therefore
The table 2 not represent a proportional relationship
Table 3
For x=1, y=50 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{50}{1}=50[/tex]
For x=3, y=150 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{150}{3}=50[/tex]
For x=4, y=200 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{200}{4}=50[/tex]
For x=5, y=250 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{250}{5}=50[/tex]
The values of k are the same
therefore
The table 3 represent a proportional relationship
Table 4
For x=1, y=1.5 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{1.5}{1}=1.5[/tex]
For x=2, y=3 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{3}{2}=1.5[/tex]
For x=3, y=6 ---> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{6}{3}=2[/tex]
The values of k are different
therefore
The table 4 not represent a proportional relationship
