To find the slope of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the points are [tex]\((1, 0)\)[/tex] and [tex]\((3, 8)\)[/tex]. Let's substitute these coordinates into the slope formula:
1. Identify the coordinates [tex]\((x_1, y_1) = (1, 0)\)[/tex] and [tex]\((x_2, y_2) = (3, 8)\)[/tex].
2. Plug the coordinates into the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
[tex]\[ m = \frac{8 - 0}{3 - 1} \][/tex]
3. Simplify the fraction:
[tex]\[ m = \frac{8}{2} \][/tex]
[tex]\[ m = 4 \][/tex]
Therefore, the slope of the line through the points [tex]\((1, 0)\)[/tex] and [tex]\((3, 8)\)[/tex] is [tex]\(4\)[/tex].
So, the correct answer is:
(D) [tex]\(4\)[/tex]
