Question

Vincent has model trains. He made these tables to compare the time during which each train moves with the distance it moves.

For which train do the numbers in the table form a proportional relationship?
A. is the 1st pic
B. is the 2nd pic
C. is the 3rd pic
D. is the 4th pic

Answer 1

Answer:

Option B. is the 2nd pic (Train 2)

Step-by-step explanation:

Let

x ----> the time in seconds

y ----> the distance in centimeters

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each table

Train 1

Find the value of k

$k=y/x$

For x=5, y=10 ----> $k=10/5=2$

For x=10, y=15 ----> $k=15/10=1.5$

For x=20, y=20 ----> $k=20/20=1$

The values of k are different

therefore

The numbers in the table not form a proportional relationship

Train 2

Find the value of k

$k=y/x$

For x=5, y=20 ----> $k=20/5=4$

For x=10, y=40 ----> $k=40/10=4$

For x=20, y=80 ----> $k=80/20=4$

The values of k are the same

therefore

The numbers in the table form a proportional relationship

Train 3

Find the value of k

$k=y/x$

For x=5, y=10 ----> $k=10/5=2$

For x=10, y=15 ----> $k=15/10=1.5$

For x=20, y=30 ----> $k=30/20=1.5$

The values of k are different

therefore

The numbers in the table not form a proportional relationship

Train 4

Find the value of k

$k=y/x$

For x=5, y=20 ----> $k=20/5=4$

For x=10, y=25 ----> $k=25/10=2.5$

For x=20, y=30 ----> $k=30/20=1.5$

The values of k are different

therefore

The numbers in the table not form a proportional relationship

Answer 2

Answer:

b.

Step-by-step explanation:

the 2nd picture