Question

Sara graphs a line passing through points that represent a proportional relationship. Which set of points could be on the line that Sara graphs?

Answer 1

The Answer is B. (6, 8), (0, 0), (18, 24)

Explanation:

A line that passes through the origin, (0, 0), represents a proportional relationship.

Answer 2

Option B). (6,8),(0,0),(18,24)

Explanation:

The options of the question are

A). (2,4),(0,2),(3,9)

B). (6,8),(0,0),(18,24)

C). (3,6),(4,8),(9,4)

D). (1,1),(2,1),(3,3)​

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 case

case A) (2,4),(0,2),(3,9)

This set of points not represent a proportional relationship because in a proportional relationship the intercepts must be equal to (0,0) and this set of points have the point (0,2)

case B) (6,8),(0,0),(18,24)

Find the constant of proportionality k

`k=(y)/(x)`

For x=6, y=8 ---->
`k=(8)/(6)=(4)/(3)`

For x=18, y=24 ---->
`k=(24)/(18)=(4)/(3)`

The line passes through the origin

The linear equation is

`y=(4)/(3)x`

so

This set of points could be n the line that Sara graphs

case C) (3,6),(4,8),(9,4)

Find the constant of proportionality k

`k=(y)/(x)`

For x=3, y=6 ---->
`k=(6)/(3)=2`

For x=4, y=8 ---->
`k=(8)/(4)=2`

For x=9, y=4 ---->
`k=(4)/(9)`

The values of k are different

therefore

This set of points not represent a proportional relationship

case D) (1,1),(2,1),(3,3)​

Find the constant of proportionality k

`k=(y)/(x)`

For x=1, y=1 ---->
`k=(1)/(1)=1`

For x=2, y=1 ---->
`k=(1)/(2)`

The values of k are different

therefore

This set of points not represent a proportional relationship