To find the slope of the line that passes through the points [tex]\((3, 8)\)[/tex] and [tex]\((-2, 13)\)[/tex], we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]. The slope (denoted as [tex]\(m\)[/tex]) is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
In this case, the points are [tex]\((3, 8)\)[/tex] and [tex]\((-2, 13)\)[/tex]. Let's identify [tex]\(x_1, y_1, x_2,\)[/tex] and [tex]\(y_2\)[/tex] from these coordinates:
- [tex]\(x_1 = 3\)[/tex]
- [tex]\(y_1 = 8\)[/tex]
- [tex]\(x_2 = -2\)[/tex]
- [tex]\(y_2 = 13\)[/tex]
Now, substitute these values into the slope formula:
[tex]\[
m = \frac{13 - 8}{-2 - 3}
\][/tex]
Calculate the differences in the numerator and the denominator:
[tex]\[
13 - 8 = 5 \quad \text{and} \quad -2 - 3 = -5
\][/tex]
So the slope formula becomes:
[tex]\[
m = \frac{5}{-5}
\][/tex]
Simplify the fraction:
[tex]\[
m = -1
\][/tex]
Thus, the slope of the line that passes through the points [tex]\((3, 8)\)[/tex] and [tex]\((-2, 13)\)[/tex] is:
[tex]\[
\boxed{-1}
\][/tex]
