Question
Which table represents the same proportional relationship as the equation y = 36 x?
A 2-column table with 4 rows. Column 1 is labeled x with entries 0.5, 2, 3, 6. Column 2 is labeled y with entries 36.5, 38, 39, 42.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0.5, 2, 3, 6. Column 2 is labeled y with entries 64, 18, 12, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0.5, 2, 3, 6. Column 2 is labeled y with entries 18, 72, 108, 216.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0.5, 2, 3, 6. Column 2 is labeled y with entries 36, 36, 36, 36.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0.5, 2, 3, 6. Column 2 is labeled y with entries 36.5, 38, 39, 42.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0.5, 2, 3, 6. Column 2 is labeled y with entries 64, 18, 12, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0.5, 2, 3, 6. Column 2 is labeled y with entries 18, 72, 108, 216.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0.5, 2, 3, 6. Column 2 is labeled y with entries 36, 36, 36, 36.
Answers
GPT-4o mini
To determine which table represents the same proportional relationship as the equation \( y = 36x \), we need to calculate \( y \) for the given \( x \) values in each table using this equation.
1. For **Table 1** with \( y \) entries 36.5, 38, 39, 42:
- \( x = 0.5 \) → \( y = 36 \times 0.5 = 18 \)
- \( x = 2 \) → \( y = 36 \times 2 = 72 \)
- \( x = 3 \) → \( y = 36 \times 3 = 108 \)
- \( x = 6 \) → \( y = 36 \times 6 = 216 \)
- The \( y \) values do not match (36.5, 38, 39, 42).
2. For **Table 2** with \( y \) entries 64, 18, 12, 6:
- The calculations do not match the equation values (as real \( y\) values would be 18, 72, 108, 216).
3. For **Table 3** with \( y \) entries 18, 72, 108, 216:
- \( x = 0.5 \) → \( y = 36 \times 0.5 = 18 \)
- \( x = 2 \) → \( y = 36 \times 2 = 72 \)
- \( x = 3 \) → \( y = 36 \times 3 = 108 \)
- \( x = 6 \) → \( y = 36 \times 6 = 216 \)
- These \( y \) values match perfectly.
4. For **Table 4** with \( y \) entries all 36:
- The calculations do not match as \( y \) should vary with \( x \).
Thus, the correct table that represents the same proportional relationship as the equation \( y = 36x \) is **Table 3**.
1. For **Table 1** with \( y \) entries 36.5, 38, 39, 42:
- \( x = 0.5 \) → \( y = 36 \times 0.5 = 18 \)
- \( x = 2 \) → \( y = 36 \times 2 = 72 \)
- \( x = 3 \) → \( y = 36 \times 3 = 108 \)
- \( x = 6 \) → \( y = 36 \times 6 = 216 \)
- The \( y \) values do not match (36.5, 38, 39, 42).
2. For **Table 2** with \( y \) entries 64, 18, 12, 6:
- The calculations do not match the equation values (as real \( y\) values would be 18, 72, 108, 216).
3. For **Table 3** with \( y \) entries 18, 72, 108, 216:
- \( x = 0.5 \) → \( y = 36 \times 0.5 = 18 \)
- \( x = 2 \) → \( y = 36 \times 2 = 72 \)
- \( x = 3 \) → \( y = 36 \times 3 = 108 \)
- \( x = 6 \) → \( y = 36 \times 6 = 216 \)
- These \( y \) values match perfectly.
4. For **Table 4** with \( y \) entries all 36:
- The calculations do not match as \( y \) should vary with \( x \).
Thus, the correct table that represents the same proportional relationship as the equation \( y = 36x \) is **Table 3**.