Answer:
The option 3 will be perfect for Relationship B.
Step-by-step explanation:
Relation A gives two points on the graph of it, and they are (2,3) and (4,6).
Therefore, the equation of A is given by [tex]\frac{y-6}{6-3} =\frac{x-4}{4-2}[/tex]
⇒ [tex]2y = 3x[/tex]
⇒ [tex]y= \frac{3}{2} x[/tex] ....... (1)
Now, relationship B is given in the table which has lesser rate i.e. lesser slope than relationship A. So, the y value for A will be higher that y value of B for the same value of x.
From equation (1), [tex]y_{x=3} = 4.5[/tex] > 2.25 only.
Now, [tex]y_{x=6} =9 > 4.5[/tex]
[tex]y_{x=8} =12 > 6[/tex]
and [tex]y_{x=10} =15 > 7.5[/tex]
Therefore, the option 3 will be perfect for Relationship B. (Answer)
Answer:
[tex]\textbf{Option C: $(3,2.25)$, $(6,4.5)$, $(8,6)$, $(107.5) $}\\[/tex]
Step-by-step explanation:[tex]\textup{It is given that B has a lesser relationship than A}.\\\\\textup{That means B would be growing lesser inches on any given week than A.}\\\\\textup{Look at the graph of A. In the sixth week, A has grown 9 inches [(6,9)].}\\\\\textup{That means B should have grown lesser than that.}\\[/tex]
[tex]\textup{In all the options except for C, we have numbers greater than 9 against 6 for B making them }[/tex] [tex]\textup{wrong}[/tex]