Question

Is the relationship between the given data points linear? If so, which of the following equations best models the data?

1.The relationship is not linear.
2.The relationship is linear; y+4=(x–1).
3.The relationship is linear; y–1=–2(x+4).
4. The relationship is linear; y+4=2(x–1).

Answer 1

The relationship between the given data points is linear, and the equation y = -2x - 7 best models the data.

Step-by-step explanation:

The relationship between the given data points is linear. This can be determined by checking if the equation y = mx + b fits the data points. Let's check the options:

1. The relationship is not linear, so this option is incorrect.
2. The equation y + 4 = x - 1 can be rewritten as y = x - 5. This equation represents a linear relationship, but it does not match the given data points. So, this option is incorrect.
3. The equation y - 1 = -2(x + 4) can be rewritten as y = -2x - 7. This equation represents a linear relationship and matches the given data points. So, this option is correct.
4. The equation y + 4 = 2(x - 1) can be rewritten as y = 2x - 6. This equation represents a linear relationship, but it does not match the given data points. So, this option is incorrect.

Therefore, the correct answer is option 3. The relationship is linear and can be represented by the equation y = -2x - 7.