Question

Which table shows a proportional relationship between X and Y?

Answer 1

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 $k=\frac{y}{x}$ or $y=kx$

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 ---> $k=\frac{y}{x}$ ----> $k=\frac{6}{2}=3$

For x=4, y=12 ---> $k=\frac{y}{x}$ ----> $k=\frac{12}{4}=3$

For x=5, y=18 ---> $k=\frac{y}{x}$ ----> $k=\frac{18}{5}=3.6$

The values of k are different

therefore

The table 1 not represent a proportional relationship

Table 2

For x=3, y=1.5 ---> $k=\frac{y}{x}$ ----> $k=\frac{1.5}{3}=0.5$

For x=5, y=2.5 ---> $k=\frac{y}{x}$ ----> $k=\frac{2.5}{5}=0.5$

For x=7, y=3 ---> $k=\frac{y}{x}$ ----> $k=\frac{3}{7}=0.4$

The values of k are different

therefore

The table 2 not represent a proportional relationship

Table 3

For x=1, y=50 ---> $k=\frac{y}{x}$ ----> $k=\frac{50}{1}=50$

For x=3, y=150 ---> $k=\frac{y}{x}$ ----> $k=\frac{150}{3}=50$

For x=4, y=200 ---> $k=\frac{y}{x}$ ----> $k=\frac{200}{4}=50$

For x=5, y=250 ---> $k=\frac{y}{x}$ ----> $k=\frac{250}{5}=50$

The values of k are the same

therefore

The table 3 represent a proportional relationship

Table 4

For x=1, y=1.5 ---> $k=\frac{y}{x}$ ----> $k=\frac{1.5}{1}=1.5$

For x=2, y=3 ---> $k=\frac{y}{x}$ ----> $k=\frac{3}{2}=1.5$

For x=3, y=6 ---> $k=\frac{y}{x}$ ----> $k=\frac{6}{3}=2$

The values of k are different

therefore

The table 4 not represent a proportional relationship