To complete the order pairs in the table based on the equation \( y = 5x \), we can calculate the \( y \) values given the \( x \) values.
For each option:
A: \( (0, 0), (5, 1), (10, 2) \)
- \( x = 0 \) → \( y = 5 \times 0 = 0 \) → (0, 0)
- \( x = 5 \) → \( y = 5 \times 5 = 25 \) → (5, 25) (not (5, 1))
- \( x = 10 \) → \( y = 5 \times 10 = 50 \) → (10, 50) (not (10, 2))
B: \( (0,0), (1,5), (2, 10) \)
- \( x = 0 \) → \( y = 5 \times 0 = 0 \) → (0, 0)
- \( x = 1 \) → \( y = 5 \times 1 = 5 \) → (1, 5)
- \( x = 2 \) → \( y = 5 \times 2 = 10 \) → (2, 10)
C: \( (0,0), (1, 5), (3, 15) \)
- \( x = 0 \) → \( y = 5 \times 0 = 0 \) → (0, 0)
- \( x = 1 \) → \( y = 5 \times 1 = 5 \) → (1, 5)
- \( x = 3 \) → \( y = 5 \times 3 = 15 \) → (3, 15)
D: \( (0, 0), (1, 1/5), (2, 2/5) \)
- \( x = 0 \) → \( y = 5 \times 0 = 0 \) → (0, 0)
- \( x = 1 \) → \( y = 5 \times 1 = 5 \) → (1, 5) (not (1, 1/5))
- \( x = 2 \) → \( y = 5 \times 2 = 10 \) → (2, 10) (not (2, 2/5))
After reviewing the calculations, we can conclude that the correct set of ordered pairs that fit the equation \( y = 5x \) is option B:
B : (0, 0), (1, 5), (2, 10)