Answer :
To determine the slope of the linear function represented in the table, we start by choosing any two points from the table of values. Let’s select the points [tex]\((-2, 8)\)[/tex] and [tex]\((-1, 2)\)[/tex].
The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
### Step-by-step:
1. Identify the Coordinates:
- Point 1: [tex]\((x_1, y_1) = (-2, 8)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (-1, 2)\)[/tex]
2. Substitute the coordinates into the slope formula:
[tex]\[ m = \frac{2 - 8}{-1 - (-2)} \][/tex]
3. Simplify the numerator and the denominator:
- Numerator: [tex]\(2 - 8 = -6\)[/tex]
- Denominator: [tex]\(-1 - (-2) = -1 + 2 = 1\)[/tex]
4. Calculate the slope:
[tex]\[ m = \frac{-6}{1} = -6 \][/tex]
Hence, the slope of the function is [tex]\(-6\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{-6} \][/tex]
The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
### Step-by-step:
1. Identify the Coordinates:
- Point 1: [tex]\((x_1, y_1) = (-2, 8)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (-1, 2)\)[/tex]
2. Substitute the coordinates into the slope formula:
[tex]\[ m = \frac{2 - 8}{-1 - (-2)} \][/tex]
3. Simplify the numerator and the denominator:
- Numerator: [tex]\(2 - 8 = -6\)[/tex]
- Denominator: [tex]\(-1 - (-2) = -1 + 2 = 1\)[/tex]
4. Calculate the slope:
[tex]\[ m = \frac{-6}{1} = -6 \][/tex]
Hence, the slope of the function is [tex]\(-6\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{-6} \][/tex]
