Question

Please explain how to find the proportional relationship.

Answer 1

Answer:

The table A represent a proportional relationship

The table B 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 $k=\frac{y}{x}$ 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

Table A

Find the value of k

For x=1,y=2 ------> $k=\frac{2}{1}=2$

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

For x=4,y=8 ------> $k=\frac{8}{4}=2$

For x=5,y=10 ------> $k=\frac{10}{5}=2$

All the values of k are the same

so

The table A represent a proportional relationship

The equation of the proportional relationship is equal to

$y=2x$

Table B

Find the value of k

For x=1,y=3 ------> $k=\frac{3}{1}=3$

For x=2,y=4 ------> $k=\frac{4}{2}=2$

The values of k are different

so

The table B not represent a proportional relationship