Answer:
Table a represent a proportional relationship
Table b represent a proportional relationship
Table c not represent a proportional relationship
Table d not represent a proportional relationship
Table e represent a proportional relationship
Table f not represent a proportional relationship
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 the constant of proportionality k for each ordered pair
If all the values of k are equal, then the table represent a proportional relationship
[tex]k=\frac{y}{x}[/tex]
Table a
For x=2, y=14 ----> [tex]k=\frac{14}{2}=7[/tex]
For x=5, y=35 ----> [tex]k=\frac{35}{5}=7[/tex]
For x=7, y=49 ----> [tex]k=\frac{49}{7}=7[/tex]
For x=10, y=70 ----> [tex]k=\frac{70}{10}=7[/tex]
All the values of k are equal
therefore
The table a represent a proportional relationship
Table b
For x=-10, y=50 ----> [tex]k=\frac{50}{-10}=-5[/tex]
For x=-2, y=10 ----> [tex]k=\frac{10}{-2}=-5[/tex]
For x=4, y=-20 ----> [tex]k=\frac{-20}{4}=-5[/tex]
For x=14, y=-70 ----> [tex]k=\frac{-70}{14}=-5[/tex]
All the values of k are equal
therefore
The table b represent a proportional relationship
Table c
For x=-1, y=-24 ----> [tex]k=\frac{-24}{-1}=24[/tex]
For x=2, y=48 ----> [tex]k=\frac{48}{2}=24[/tex]
For x=4, y=90 ----> [tex]k=\frac{90}{4}=22.5[/tex]
For x=8, y=192 ----> [tex]k=\frac{192}{8}=24[/tex]
All the values of k are not equal
therefore
The table c not represent a proportional relationship
Table d
For x=-6, y=12 ----> [tex]k=\frac{12}{-6}=-2[/tex]
For x=-3, y=6 ----> [tex]k=\frac{6}{-3}=-2[/tex]
For x=3, y=-6 ----> [tex]k=\frac{-6}{3}=-2[/tex]
For x=6, y=-10 ----> [tex]k=\frac{-10}{6}=-1.67[/tex]
All the values of k are not equal
therefore
The table d not represent a proportional relationship
Table e
For x=2, y=13.5 ----> [tex]k=\frac{13.5}{2}=6.75[/tex]
For x=5, y=33.75 ----> [tex]k=\frac{33.75}{5}=6.75[/tex]
For x=10, y=67.5 ----> [tex]k=\frac{67.5}{10}=6.75[/tex]
For x=15, y=101.25 ----> [tex]k=\frac{101.25}{15}=6.75[/tex]
All the values of k are equal
therefore
The table e represent a proportional relationship
Table f
For x=-4, y=-38 ----> [tex]k=\frac{-38}{-4}=9.5[/tex]
For x=-1, y=-9.5 ----> [tex]k=\frac{-9.5}{-1}=9.5[/tex]
For x=2, y=19 ----> [tex]k=\frac{19}{2}=9.5[/tex]
For x=3, y=27 ----> [tex]k=\frac{27}{3}=9[/tex]
All the values of k are not equal
therefore
The table f not represent a proportional relationship
