To find the slope of the line that passes through the points [tex]\((-3, -1)\)[/tex] and [tex]\( (3, 3) \)[/tex], we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the coordinates of the points are:
[tex]\( (x_1, y_1) = (-3, -1) \)[/tex]
[tex]\( (x_2, y_2) = (3, 3) \)[/tex]
Substituting these values into the slope formula, we get:
[tex]\[
\text{slope} = \frac{3 - (-1)}{3 - (-3)}
\][/tex]
Simplify the expressions inside the numerator and the denominator:
[tex]\[
\text{slope} = \frac{3 + 1}{3 + 3}
\][/tex]
[tex]\[
\text{slope} = \frac{4}{6}
\][/tex]
Reduce the fraction to its simplest form:
[tex]\[
\text{slope} = \frac{2}{3}
\][/tex]
So, the slope of the line that contains the points [tex]\((-3, -1)\)[/tex] and [tex]\( (3, 3) \)[/tex] is:
[tex]\[
\boxed{\frac{2}{3}}
\][/tex]
