Let's determine the slope of the line passing through the given points [tex]\((5, -3)\)[/tex], [tex]\((6, -1)\)[/tex], [tex]\((7, 1)\)[/tex], and [tex]\((8, 3)\)[/tex].
The slope formula for a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
First, we choose the points [tex]\((5, -3)\)[/tex] and [tex]\((6, -1)\)[/tex] from the given set. Let [tex]\((x_1, y_1) = (5, -3)\)[/tex] and [tex]\((x_2, y_2) = (6, -1)\)[/tex].
Calculate the differences between the x-coordinates and the y-coordinates:
[tex]\[
x_2 - x_1 = 6 - 5 = 1
\][/tex]
[tex]\[
y_2 - y_1 = -1 - (-3) = -1 + 3 = 2
\][/tex]
Next, we use these differences to find the slope:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2}{1} = 2
\][/tex]
Therefore, the slope of the line that contains the given points is:
[tex]\[
\boxed{2}
\][/tex]
