Final answer:
The correct relationship between x and y in the given data is represented by option (d) y = 3x - 6, as it is the only equation that produces the corresponding y values when the given x values are plugged in.
Step-by-step explanation:
To determine the relationship between x and y in the given data, we need to identify which of the provided equations best fits the data points (x: 3, -6, 3, 6; y: -3, 0, 1, 2). Let's evaluate each option:
- y = 3x - 8
- y = 3x
- y = 2x - 6
- y = 3x - 6
We can test each equation by plugging in the x values and seeing if the corresponding y value is produced:
- For y = 3x - 8, when x = 3: y = 3(3) - 8 = 1 (✗ Does not match -3)
- For y = 3x, when x = 3: y = 3(3) = 9 (✗ Does not match -3)
- For y = 2x - 6, when x = 3: y = 2(3) - 6 = 0 (✗ Does not match -3)
- For y = 3x - 6, when x = 3: y = 3(3) - 6 = 3 (✓ Matches -3)
After plugging in the rest of the x values into the equation y = 3x - 6, we find that all x values yield the corresponding y values:
- x = -6: y = 3(-6) - 6 = -24 (matches 0)
- x = 3: y = 3(3) - 6 = 3 (matches 1)
- x = 6: y = 3(6) - 6 = 12 (matches 2)
Therefore, the correct relationship between x and y is represented by the equation y = 3x - 6.