Answer:
last fourth table given in the figure shows the proportional relationship .
Step-by-step explanation:
Definition of proportional relationship
The relationship in which two quantities are varies proportional to each other .
[tex]a = kb[/tex]
Where k is called the proportional constant .
Let us assume that the number of miles travelled be y .
let us assume that the gas used be x .
[tex]y\propto x[/tex]
y = ca
Where c is the proportional constant .
In first table
Miles travelled = 27.3 mi
Gas used =1.5 gal
Putting in the formula
y = ca
27.3 = 1.5c
[tex]\frac{27.3}{1.5}=c[/tex]
c = 18.2
Miles travelled = 49.16 mi
Gas used = 3.8 gal
Putting in the formula
y = ca
49.16 = 3.8c
[tex]\frac{49.16}{3.8}=c[/tex]
c = 12.94 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Second Part
Miles travelled = 135 mi
Gas used = 7.4 gal
Putting in the formula
y = ca
135 = 7.4c
[tex]\frac{135}{7.4}=c[/tex]
c = 18.2
Miles travelled = 135.5 mi
Gas used = 7.9 gal
Putting in the formula
y = ca
135.5 = 7.9c
[tex]\frac{135.5}{7.9}=c[/tex]
c = 17.2 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Third table
Miles travelled = 120 mi
Gas used = 6.2 gal
Putting in the formula
y = ca
120 = 6.2c
[tex]\frac{120}{6.2}=c[/tex]
c = 19.4 (Approx)
Miles travelled = 180 mi
Gas used = 12.2 gal
Putting in the formula
y = ca
180 = 12.2c
[tex]\frac{180}{12.2}=c[/tex]
c = 14.8 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Fourth table
Miles travelled = 270 mi
Gas used = 15gal
Putting in the formula
y = ca
270 = 15c
[tex]\frac{270}{15}=c[/tex]
c = 18
Miles travelled = 135 mi
Gas used = 7.5 gal
Putting in the formula
y = ca
135= 7.5c
[tex]\frac{135}{7.5}=c[/tex]
c = 18
Thus the miles travelled is vary with the gas used .
Therefore table shows the proportional relationship .
The last fourth table given in the figure shows the proportional relationship .
