Question

determine if these are liner relationships or not
(-2,2)(-1,0)(0,0)(1,2)(2,6)(3,12)

Answer 1

To determine if the set of points \((-2, 2)\), \((-1, 0)\), \((0, 0)\), \((1, 2)\), \((2, 6)\), and \((3, 12)\) represents a linear relationship, we can check if the slope between any two points is constant.

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's compute the slopes between consecutive points:

1. Between \((-2, 2)\) and \((-1, 0)\):
\[
\text{slope} = \frac{0 - 2}{-1 - (-2)} = \frac{-2}{1} = -2
\]

2. Between \((-1, 0)\) and \((0, 0)\):
\[
\text{slope} = \frac{0 - 0}{0 - (-1)} = \frac{0}{1} = 0
\]

3. Between \((0, 0)\) and \((1, 2)\):
\[
\text{slope} = \frac{2 - 0}{1 - 0} = \frac{2}{1} = 2
\]

4. Between \((1, 2)\) and \((2, 6)\):
\[
\text{slope} = \frac{6 - 2}{2 - 1} = \frac{4}{1} = 4
\]

5. Between \((2, 6)\) and \((3, 12)\):
\[
\text{slope} = \frac{12 - 6}{3 - 2} = \frac{6}{1} = 6
\]

Since the slopes between the points are not constant (they vary from -2 to 0 to 2 to 4 to 6), we can conclude that the set of points does not represent a linear relationship.

### Conclusion:
The relationship represented by the given points is **not linear**.