Answer :
To determine the slope of the linear relationship given in the table, we need to use the points provided to calculate the slope. The slope ([tex]\(m\)[/tex]) between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Using the points from the table:
1. Calculate the slope between the points [tex]\((6, -2)\)[/tex] and [tex]\((2, 2)\)[/tex]:
[tex]\[ m_1 = \frac{2 - (-2)}{2 - 6} = \frac{2 + 2}{2 - 6} = \frac{4}{-4} = -1 \][/tex]
2. Calculate the slope between the points [tex]\((2, 2)\)[/tex] and [tex]\((0, 4)\)[/tex]:
[tex]\[ m_2 = \frac{4 - 2}{0 - 2} = \frac{4 - 2}{-2} = \frac{2}{-2} = -1 \][/tex]
3. Calculate the slope between the points [tex]\((0, 4)\)[/tex] and [tex]\((-2, 6)\)[/tex]:
[tex]\[ m_3 = \frac{6 - 4}{-2 - 0} = \frac{6 - 4}{-2} = \frac{2}{-2} = -1 \][/tex]
Since the slopes between all points are the same ([tex]\(m_1 = m_2 = m_3 = -1\)[/tex]), we can confirm that the slope of the linear relationship is consistent.
Therefore, the slope of the relationship given in the table is:
[tex]\[ \boxed{-1} \][/tex]
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Using the points from the table:
1. Calculate the slope between the points [tex]\((6, -2)\)[/tex] and [tex]\((2, 2)\)[/tex]:
[tex]\[ m_1 = \frac{2 - (-2)}{2 - 6} = \frac{2 + 2}{2 - 6} = \frac{4}{-4} = -1 \][/tex]
2. Calculate the slope between the points [tex]\((2, 2)\)[/tex] and [tex]\((0, 4)\)[/tex]:
[tex]\[ m_2 = \frac{4 - 2}{0 - 2} = \frac{4 - 2}{-2} = \frac{2}{-2} = -1 \][/tex]
3. Calculate the slope between the points [tex]\((0, 4)\)[/tex] and [tex]\((-2, 6)\)[/tex]:
[tex]\[ m_3 = \frac{6 - 4}{-2 - 0} = \frac{6 - 4}{-2} = \frac{2}{-2} = -1 \][/tex]
Since the slopes between all points are the same ([tex]\(m_1 = m_2 = m_3 = -1\)[/tex]), we can confirm that the slope of the linear relationship is consistent.
Therefore, the slope of the relationship given in the table is:
[tex]\[ \boxed{-1} \][/tex]
