Question

Which table shows a proportional relationship between miles traveled and gas used?

Answer 1

270/15 = 135/ 7.5
cross multiply to see if it is a true proportion
(15)(135) = (270)(7.5)
2025 = 2025 (correct...so this is a true proportion)

answer is : bottom right one

Answer 2

last fourth table given in the figure shows the proportional relationship .

Explanation:

Definition of proportional relationship

The relationship in which two quantities are varies proportional to each other .

`a = kb`

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 .

`y\propto x`

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

`(27.3)/(1.5)=c`

c = 18.2

Miles travelled = 49.16 mi

Gas used = 3.8 gal

Putting in the formula

y = ca

49.16 = 3.8c

`(49.16)/(3.8)=c`

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

`(135)/(7.4)=c`

c = 18.2

Miles travelled = 135.5 mi

Gas used = 7.9 gal

Putting in the formula

y = ca

135.5 = 7.9c

`(135.5)/(7.9)=c`

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

`(120)/(6.2)=c`

c = 19.4 (Approx)

Miles travelled = 180 mi

Gas used = 12.2 gal

Putting in the formula

y = ca

180 = 12.2c

`(180)/(12.2)=c`

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

`(270)/(15)=c`

c = 18

Miles travelled = 135 mi

Gas used = 7.5 gal

Putting in the formula

y = ca

135= 7.5c

`(135)/(7.5)=c`

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 .