To determine the slope of a line that passes through two points in the [tex]\(xy\)[/tex]-plane, we use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the coordinates of the two points are given as:
[tex]\[
(x_1, y_1) = (-3, -5)
\][/tex]
[tex]\[
(x_2, y_2) = (1, 7)
\][/tex]
Substitute these coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{7 - (-5)}{1 - (-3)}
\][/tex]
First, simplify the numerator:
[tex]\[
7 - (-5) = 7 + 5 = 12
\][/tex]
Next, simplify the denominator:
[tex]\[
1 - (-3) = 1 + 3 = 4
\][/tex]
Now, we can compute the slope:
[tex]\[
\text{slope} = \frac{12}{4} = 3.0
\][/tex]
Therefore, the slope of the line that passes through the points [tex]\((-3, -5)\)[/tex] and [tex]\((1, 7)\)[/tex] is:
[tex]\[
\boxed{3}
\][/tex]
