Answer:
b
Explanation:
To determine which equation represents the relationship shown in the table, we can substitute the x-values from the table into each equation and see which one gives the corresponding y-values.
Let's evaluate each equation:
A. y = x + 1
- For x = -2, y = -2 + 1 = -1
- For x = 0, y = 0 + 1 = 1
- For x = 1, y = 1 + 1 = 2
- For x = 3, y = 3 + 1 = 4
- For x = 4, y = 4 + 1 = 5
B. y = -2x + 6
- For x = -2, y = -2(-2) + 6 = 4 + 6 = 10
- For x = 0, y = -2(0) + 6 = 0 + 6 = 6
- For x = 1, y = -2(1) + 6 = -2 + 6 = 4
- For x = 3, y = -2(3) + 6 = -6 + 6 = 0
- For x = 4, y = -2(4) + 6 = -8 + 6 = -2
C. y = -x - 6
- For x = -2, y = -(-2) - 6 = 2 - 6 = -4
- For x = 0, y = -(0) - 6 = 0 - 6 = -6
- For x = 1, y = -(1) - 6 = -1 - 6 = -7
- For x = 3, y = -(3) - 6 = -3 - 6 = -9
- For x = 4, y = -(4) - 6 = -4 - 6 = -10
D. y = 2x - 1
- For x = -2, y = 2(-2) - 1 = -4 - 1 = -5
- For x = 0, y = 2(0) - 1 = 0 - 1 = -1
- For x = 1, y = 2(1) - 1 = 2 - 1 = 1
- For x = 3, y = 2(3) - 1 = 6 - 1 = 5
- For x = 4, y = 2(4) - 1 = 8 - 1 = 7
Based on the evaluation, the equation that matches the y-values in the table is:
B. y = -2x + 6
So, the answer is B.