Which table represents the same proportional relationship as the equation y = 36 x?

Question

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.

Answer 1

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.