At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

A linear relationship is given in the table.

| [tex]\(x\)[/tex] | [tex]\(y\)[/tex] |
|------|------|
| 6 | -2 |
| 2 | 2 |
| 0 | 4 |
| -2 | 6 |

What is the slope of the relationship?

A. -2
B. -1
C. 1
D. 2


Sagot :

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]