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].



Answer :

To find the slope of the line that passes through two given points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], you can use the slope formula:

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

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

1. Assign the coordinates:
- [tex]\((x_1, y_1) = (-14, 8)\)[/tex]
- [tex]\((x_2, y_2) = (14, 0)\)[/tex]

2. Substitute the coordinates into the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 8}{14 - (-14)} \][/tex]

3. Simplify the expressions inside the numerator and denominator:
- Numerator: [tex]\(0 - 8 = -8\)[/tex]
- Denominator: [tex]\(14 - (-14) = 14 + 14 = 28\)[/tex]

4. Calculate the division to find the slope:
[tex]\[ \text{slope} = \frac{-8}{28} \][/tex]

5. Simplify the fraction:
[tex]\[ \text{slope} = \frac{-8}{28} = -0.2857142857142857 \][/tex]

Therefore, the slope of the line that passes through the points in the table is [tex]\(-0.2857142857142857\)[/tex].