Question

determine if these are liner relationships or not
(-2,-4)(-1,1)(0,0)(1,1)(2,4)(3,9)

Answer 1

To determine if the points \((-2, -4)\), \((-1, 1)\), \((0, 0)\), \((1, 1)\), \((2, 4)\), and \((3, 9)\) represent a linear relationship, you need to check if they all lie on a straight line. One way to do this is to calculate the slope between consecutive points and see if the slopes are the same.

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

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

Let's calculate the slopes between consecutive points:

1. Between \((-2, -4)\) and \((-1, 1)\):
\[
m = \frac{1 - (-4)}{-1 - (-2)} = \frac{5}{1} = 5
\]

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

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

4. Between \((1, 1)\) and \((2, 4)\):
\[
m = \frac{4 - 1}{2 - 1} = \frac{3}{1} = 3
\]

5. Between \((2, 4)\) and \((3, 9)\):
\[
m = \frac{9 - 4}{3 - 2} = \frac{5}{1} = 5
\]

The slopes obtained from the pairs of points are \(5\), \(-1\), \(1\), \(3\), and \(5\), which are not all equal. Because the slopes between consecutive points are different, the points do not lie on a straight line.

Therefore, the set of points does not represent a linear relationship.