Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To determine which table of ordered pairs represents a proportional relationship, we need to check if the ratio [tex]\( \frac{y}{x} \)[/tex] is constant for all pairs in each table. This means that if you divide [tex]\( y \)[/tex] by [tex]\( x \)[/tex] for each pair in the table, the result should be the same for every pair (excluding pairs where [tex]\( x \)[/tex] is zero because division by zero is undefined).
Let's check each table one by one:
1. Table 1:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 0 & 10 \\ \hline 5 & 20 \\ \hline 10 & 30 \\ \hline \end{tabular} \][/tex]
- Pair (5, 20): [tex]\( \frac{20}{5} = 4 \)[/tex]
- Pair (10, 30): [tex]\( \frac{30}{10} = 3 \)[/tex]
The ratios 4 and 3 are not the same, so this table does not represent a proportional relationship.
2. Table 2:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 10 \\ \hline 4 & 20 \\ \hline 6 & 30 \\ \hline \end{tabular} \][/tex]
- Pair (2, 10): [tex]\( \frac{10}{2} = 5 \)[/tex]
- Pair (4, 20): [tex]\( \frac{20}{4} = 5 \)[/tex]
- Pair (6, 30): [tex]\( \frac{30}{6} = 5 \)[/tex]
All ratios are 5, so this table does represent a proportional relationship.
3. Table 3:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 1 & 2 \\ \hline 2 & 3 \\ \hline 3 & 4 \\ \hline \end{tabular} \][/tex]
- Pair (1, 2): [tex]\( \frac{2}{1} = 2 \)[/tex]
- Pair (2, 3): [tex]\( \frac{3}{2} = 1.5 \)[/tex]
- Pair (3, 4): [tex]\( \frac{4}{3} \approx 1.33 \)[/tex]
The ratios 2, 1.5, and approximately 1.33 are not the same, so this table does not represent a proportional relationship.
4. Table 4:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 1 & 4 \\ \hline 3 & 10 \\ \hline 4 & 13 \\ \hline \end{tabular} \][/tex]
- Pair (1, 4): [tex]\( \frac{4}{1} = 4 \)[/tex]
- Pair (3, 10): [tex]\( \frac{10}{3} \approx 3.33 \)[/tex]
- Pair (4, 13): [tex]\( \frac{13}{4} = 3.25 \)[/tex]
The ratios 4, approximately 3.33, and 3.25 are not the same, so this table does not represent a proportional relationship.
Thus, the table that represents a proportional relationship is Table 2.
Let's check each table one by one:
1. Table 1:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 0 & 10 \\ \hline 5 & 20 \\ \hline 10 & 30 \\ \hline \end{tabular} \][/tex]
- Pair (5, 20): [tex]\( \frac{20}{5} = 4 \)[/tex]
- Pair (10, 30): [tex]\( \frac{30}{10} = 3 \)[/tex]
The ratios 4 and 3 are not the same, so this table does not represent a proportional relationship.
2. Table 2:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 10 \\ \hline 4 & 20 \\ \hline 6 & 30 \\ \hline \end{tabular} \][/tex]
- Pair (2, 10): [tex]\( \frac{10}{2} = 5 \)[/tex]
- Pair (4, 20): [tex]\( \frac{20}{4} = 5 \)[/tex]
- Pair (6, 30): [tex]\( \frac{30}{6} = 5 \)[/tex]
All ratios are 5, so this table does represent a proportional relationship.
3. Table 3:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 1 & 2 \\ \hline 2 & 3 \\ \hline 3 & 4 \\ \hline \end{tabular} \][/tex]
- Pair (1, 2): [tex]\( \frac{2}{1} = 2 \)[/tex]
- Pair (2, 3): [tex]\( \frac{3}{2} = 1.5 \)[/tex]
- Pair (3, 4): [tex]\( \frac{4}{3} \approx 1.33 \)[/tex]
The ratios 2, 1.5, and approximately 1.33 are not the same, so this table does not represent a proportional relationship.
4. Table 4:
[tex]\[ \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 1 & 4 \\ \hline 3 & 10 \\ \hline 4 & 13 \\ \hline \end{tabular} \][/tex]
- Pair (1, 4): [tex]\( \frac{4}{1} = 4 \)[/tex]
- Pair (3, 10): [tex]\( \frac{10}{3} \approx 3.33 \)[/tex]
- Pair (4, 13): [tex]\( \frac{13}{4} = 3.25 \)[/tex]
The ratios 4, approximately 3.33, and 3.25 are not the same, so this table does not represent a proportional relationship.
Thus, the table that represents a proportional relationship is Table 2.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
