Use the values in the table to determine the slope.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-4 & 19 \\
\hline
-2 & 16 \\
\hline
0 & 13 \\
\hline
2 & 10 \\
\hline
4 & 7 \\
\hline
\end{tabular}

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

A. none
B. [tex]\(\frac{3}{2}\)[/tex]
C. 0
D. [tex]\(-\frac{3}{2}\)[/tex]



Answer :

To determine the slope using the values given in the table, we will employ the formula for the slope between two points [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex]:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

From the table, we can choose any pair of points to calculate the slope. However, we'll use the points [tex]\((x_1, y_1) = (-4, 19)\)[/tex] and [tex]\((x_2, y_2) = (4, 7)\)[/tex].

Now, we substitute these values into the slope formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

[tex]\[ m = \frac{7 - 19}{4 - (-4)} \][/tex]

[tex]\[ m = \frac{7 - 19}{4 + 4} \][/tex]

[tex]\[ m = \frac{-12}{8} \][/tex]

[tex]\[ m = -\frac{12}{8} \][/tex]

Simplifying the fraction, we get:

[tex]\[ m = -\frac{3}{2} \][/tex]

Therefore, the slope [tex]\(m\)[/tex] is:

[tex]\[ m = -\frac{3}{2} \][/tex]

So, the correct answer is:

[tex]\[ -\frac{3}{2} \][/tex]