Which set of values could be from a direct proportion?
Accepted Solution
A:
Answer:First tableStep-by-step explanation:We have to find the set of value which could be from a direct proportion.We know that Direct proportion : When x is directly proportional to y[tex]x\propto y[/tex][tex]x=ky[/tex]Where k=Proportionality constant[tex]k=\frac{x}{y}[/tex]K remain constant when x and y are in direct proportionFrom first table[tex]k=\frac{\frac{1}{2}}{6}=\frac{1}{12}[/tex][tex]k=\frac{1}{12}[/tex][tex]k=\frac{2}{24}=\frac{1}{12}[/tex][tex]K=\frac{3}{36}=\frac{1}{12}[/tex]When x and y are both varies then ratio of x and y remain constant.Hence, it is in direct proportion.From second table[tex]k=\frac{0}{0}=[/tex] not ]define[tex]k=\frac{1}{1}=1[/tex]It is not direct proportion because k does not remain constant.From third table[tex]k=\frac{0}{2}=0[/tex][tex]k=\frac{2}{4}=\frac{1}{2}[/tex]It is not direct proportion because k does not remain constant.