Get the information you need with the help of IDNLearn.com's expert community. Our community is here to provide detailed and trustworthy answers to any questions you may have.
Sagot :
To determine if there is a proportional relationship between the variables \( x \) and \( y \) given in the table, we need to check if the ratio \(\frac{y}{x}\) is constant for all pairs \((x, y)\).
We'll evaluate the ratio for each pair of values:
1. For \( x = \frac{1}{4} \) and \( y = 3 \):
[tex]\[ \frac{y}{x} = \frac{3}{\frac{1}{4}} = 3 \times 4 = 12 \][/tex]
2. For \( x = \frac{2}{4} \) (which simplifies to \(\frac{1}{2}\)) and \( y = 6 \):
[tex]\[ \frac{y}{x} = \frac{6}{\frac{1}{2}} = 6 \times 2 = 12 \][/tex]
3. For \( x = \frac{3}{4} \) and \( y = 9 \):
[tex]\[ \frac{y}{x} = \frac{9}{\frac{3}{4}} = 9 \times \frac{4}{3} = 12 \][/tex]
Since the ratio \(\frac{y}{x}\) is constant and is equal to 12 for all given pairs of \((x, y)\), we can conclude that there is a proportional relationship between \( x \) and \( y \).
Therefore, the answer is:
(A) Yes
We'll evaluate the ratio for each pair of values:
1. For \( x = \frac{1}{4} \) and \( y = 3 \):
[tex]\[ \frac{y}{x} = \frac{3}{\frac{1}{4}} = 3 \times 4 = 12 \][/tex]
2. For \( x = \frac{2}{4} \) (which simplifies to \(\frac{1}{2}\)) and \( y = 6 \):
[tex]\[ \frac{y}{x} = \frac{6}{\frac{1}{2}} = 6 \times 2 = 12 \][/tex]
3. For \( x = \frac{3}{4} \) and \( y = 9 \):
[tex]\[ \frac{y}{x} = \frac{9}{\frac{3}{4}} = 9 \times \frac{4}{3} = 12 \][/tex]
Since the ratio \(\frac{y}{x}\) is constant and is equal to 12 for all given pairs of \((x, y)\), we can conclude that there is a proportional relationship between \( x \) and \( y \).
Therefore, the answer is:
(A) Yes
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.