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Find the slope of the line that passes through the points shown in the table.

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-14 & 8 \\
\hline
-7 & 6 \\
\hline
0 & 4 \\
\hline
7 & 2 \\
\hline
14 & 0 \\
\hline
\end{tabular}
\][/tex]

The slope of the line that passes through the points in the table is [tex]\(\square\)[/tex].


Sagot :

To find the slope of the line that passes through the points shown in the table, we need to use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

We can select any two points from the table to calculate the slope. Let's use the points [tex]\((-14, 8)\)[/tex] and [tex]\( (14, 0) \)[/tex].

Using these points, we identify:
- [tex]\( (x_1, y_1) = (-14, 8) \)[/tex]
- [tex]\( (x_2, y_2) = (14, 0) \)[/tex]

Now, substitute these values into the slope formula:
[tex]\[ m = \frac{0 - 8}{14 - (-14)} \][/tex]

Next, let's simplify the expression:
[tex]\[ m = \frac{0 - 8}{14 + 14} \][/tex]
[tex]\[ m = \frac{-8}{28} \][/tex]
[tex]\[ m = -0.2857142857142857 \][/tex]

Thus, the slope of the line that passes through the points in the table is:
[tex]\[ \boxed{-0.2857142857142857} \][/tex]