The table represents a linear function.

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

What is the slope of the function?

A. [tex]$-6$[/tex]

B. [tex]$-4$[/tex]

C. [tex]$4$[/tex]

D. [tex]$6$[/tex]



Answer :

To determine the slope of the linear function represented by the table, we need to use the slope formula which is calculated as the change in y divided by the change in x. This formula is written as:

[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} \][/tex]

where \(\Delta y\) represents the change in the y-values, and \(\Delta x\) represents the change in the x-values.

Let's take the first two points from the table to find the slope:

The points are:
[tex]\[ (x_1, y_1) = (-2, 8) \][/tex]
[tex]\[ (x_2, y_2) = (-1, 2) \][/tex]

Now, calculate the change in y (\(\Delta y\)) and the change in x (\(\Delta x\)):
[tex]\[ \Delta y = y_2 - y_1 = 2 - 8 = -6 \][/tex]
[tex]\[ \Delta x = x_2 - x_1 = -1 - (-2) = -1 + 2 = 1 \][/tex]

Next, we substitute these values into the slope formula:
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{-6}{1} = -6.0 \][/tex]

Therefore, the slope of the function is:

[tex]\[ -6.0 \][/tex]

So, the correct option is:

[tex]\[ -6 \][/tex]