Sure! Let's determine the slope of the line passing through the points [tex]\((-3, -5)\)[/tex] and [tex]\((1, 7)\)[/tex].
The slope [tex]\(m\)[/tex] of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, our points are [tex]\((x_1, y_1) = (-3, -5)\)[/tex] and [tex]\((x_2, y_2) = (1, 7)\)[/tex].
So we substitute these into the formula:
[tex]\[
m = \frac{7 - (-5)}{1 - (-3)}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{7 + 5}{1 + 3}
\][/tex]
[tex]\[
m = \frac{12}{4}
\][/tex]
[tex]\[
m = 3
\][/tex]
Therefore, the slope of the line passing through the points [tex]\((-3, -5)\)[/tex] and [tex]\((1, 7)\)[/tex] is [tex]\(3\)[/tex].
Hence, the correct answer is:
(B) 3
