The table represents a linear function.

[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 8 \\
\hline
-1 & 2 \\
\hline
0 & -4 \\
\hline
1 & -10 \\
\hline
2 & -16 \\
\hline
\end{array}
\][/tex]

What is the slope of the function?

A. -6
B. -4
C. 4



Answer :

To determine the slope of the linear function represented by the given table, follow these steps:

1. Select any two points from the table. Let's choose the points [tex]\((-2, 8)\)[/tex] and [tex]\((-1, 2)\)[/tex].

2. Use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are two points on the line.

3. Plug in the coordinates of the selected points into the formula. For the points [tex]\((-2, 8)\)[/tex] and [tex]\((-1, 2)\)[/tex]:
[tex]\[ x_1 = -2, \quad y_1 = 8, \quad x_2 = -1, \quad y_2 = 2 \][/tex]

4. Substitute these values into the slope formula:
[tex]\[ \text{slope} = \frac{2 - 8}{-1 - (-2)} = \frac{-6}{1} = -6 \][/tex]

5. Therefore, the slope of the function is [tex]\(-6\)[/tex].

So the correct option is:
[tex]\[ -6 \][/tex]