To determine the slope of the line that passes through the points [tex]\((-3, -1)\)[/tex] and [tex]\( (3, -10) \)[/tex], we can use the slope formula. The slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, our points are [tex]\((x_1, y_1) = (-3, -1)\)[/tex] and [tex]\((x_2, y_2) = (3, -10)\)[/tex].
Substitute the coordinates into the slope formula:
[tex]\[
m = \frac{-10 - (-1)}{3 - (-3)}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{-10 + 1}{3 + 3}
\][/tex]
[tex]\[
m = \frac{-9}{6}
\][/tex]
Simplify the fraction:
[tex]\[
m = \frac{-9}{6} = -\frac{3}{2}
\][/tex]
Hence, the slope of the line that contains the points [tex]\((-3, -1)\)[/tex] and [tex]\((3, -10)\)[/tex] is [tex]\( -\frac{3}{2} \)[/tex].
Correct answer: [tex]\( -\frac{3}{2} \)[/tex]
