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 [tex]y/x=k[/tex] or [tex]y=kx[/tex]
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
[tex]k=\frac{y}{x}[/tex]
For x=6, y=8 ----> [tex]k=\frac{8}{6}=\frac{4}{3}[/tex]
For x=18, y=24 ----> [tex]k=\frac{24}{18}=\frac{4}{3}[/tex]
The line passes through the origin
The linear equation is
[tex]y=\frac{4}{3}x[/tex]
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
[tex]k=\frac{y}{x}[/tex]
For x=3, y=6 ----> [tex]k=\frac{6}{3}=2[/tex]
For x=4, y=8 ----> [tex]k=\frac{8}{4}=2[/tex]
For x=9, y=4 ----> [tex]k=\frac{4}{9}[/tex]
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
[tex]k=\frac{y}{x}[/tex]
For x=1, y=1 ----> [tex]k=\frac{1}{1}=1[/tex]
For x=2, y=1 ----> [tex]k=\frac{1}{2}[/tex]
The values of k are different
therefore
This set of points not represent a proportional relationship
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.
