Which function rule represents the data in the table below?
Input(x) 1 2 3 4 5
Output (y) 9 14 19 24 29
y = 4 + 5x
y = 3 + 6x
y = 5 + 4x
y = 6 + 3x
y = 4 + 5x
To determine which function rule represents the data in the table, we can compare the input and output values by substituting them into the given function rules.
Let's check each option:
1. y = 4 + 5x
- When x = 1, y = 4 + 5(1) = 4 + 5 = 9
- When x = 2, y = 4 + 5(2) = 4 + 10 = 14
- When x = 3, y = 4 + 5(3) = 4 + 15 = 19
- When x = 4, y = 4 + 5(4) = 4 + 20 = 24
- When x = 5, y = 4 + 5(5) = 4 + 25 = 29
2. y = 3 + 6x
- When x = 1, y = 3 + 6(1) = 3 + 6 = 9
- When x = 2, y = 3 + 6(2) = 3 + 12 = 15 ≠ 14 (incorrect)
3. y = 5 + 4x
- When x = 1, y = 5 + 4(1) = 5 + 4 = 9
- When x = 2, y = 5 + 4(2) = 5 + 8 = 13 ≠ 14 (incorrect)
4. y = 6 + 3x
- When x = 1, y = 6 + 3(1) = 6 + 3 = 9
- When x = 2, y = 6 + 3(2) = 6 + 6 = 12 ≠ 14 (incorrect)
Therefore, the correct function rule that represents the data in the table is y = 4 + 5x.