To determine the slope of the linear relationship given in the table, we need to use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], which is:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's select the first two points from the table:
- Point 1: [tex]\((2, 5)\)[/tex]
- Point 2: [tex]\((1, 2)\)[/tex]
Now, we calculate the differences in their [tex]\(y\)[/tex]-coordinates and [tex]\(x\)[/tex]-coordinates:
[tex]\[ \Delta y = y_2 - y_1 = 2 - 5 = -3 \][/tex]
[tex]\[ \Delta x = x_2 - x_1 = 1 - 2 = -1 \][/tex]
Using these differences, we can now find the slope:
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{-3}{-1} = 3 \][/tex]
Therefore, the slope of the relationship is:
[tex]\[ 3 \][/tex]
So, the correct answer is:
[tex]\[ 3 \][/tex]
