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].
