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

Answer:

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

Step-by-step explanation:

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

Answer 2

Answer:

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

Step-by-step 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

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

For x=6, y=8 ----> $k=\frac{8}{6}=\frac{4}{3}$

For x=18, y=24 ----> $k=\frac{24}{18}=\frac{4}{3}$

The line passes through the origin

The linear equation is

$y=\frac{4}{3}x$

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

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

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

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

For x=9, y=4 ----> $k=\frac{4}{9}$

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

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

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

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

The values of k are different

therefore

This set of points not represent a proportional relationship