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What is the slope of the linear relationship shown in this table of values?

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-4 & 11 \\
\hline
2 & -1 \\
\hline
5 & -7 \\
\hline
\end{tabular}

A. -3

B. -2

C. 2

D. 3

Sagot :

GinnyAnswer
To determine the slope of the linear relationship given in the table of values, we can use 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]

Here are the given points from the table:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -4 & 11 \\ \hline 2 & -1 \\ \hline 5 & -7 \\ \hline \end{array} \][/tex]

First, we calculate the slope using the points [tex]\((-4, 11)\)[/tex] and [tex]\((2, -1)\)[/tex].

[tex]\[ m = \frac{-1 - 11}{2 - (-4)} = \frac{-1 - 11}{2 + 4} = \frac{-12}{6} = -2 \][/tex]

Next, we should confirm that the same slope applies between the points [tex]\((2, -1)\)[/tex] and [tex]\((5, -7)\)[/tex].

[tex]\[ m = \frac{-7 - (-1)}{5 - 2} = \frac{-7 + 1}{5 - 2} = \frac{-6}{3} = -2 \][/tex]

Since the slope between both pairs of points is the same [tex]\(-2\)[/tex], we can conclude that this is the slope of the linear relationship.

Thus, the correct answer is:

B. -2
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