To find the slope of the line containing the points [tex]\((-3, 5)\)[/tex] and [tex]\((6, -1)\)[/tex], we can use the slope formula. The slope [tex]\( m \)[/tex] of a line given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is calculated as
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's substitute the given points [tex]\((x_1, y_1) = (-3, 5)\)[/tex] and [tex]\((x_2, y_2) = (6, -1)\)[/tex] into the formula.
First, calculate the difference in the [tex]\( y \)[/tex]-coordinates:
[tex]\[
y_2 - y_1 = -1 - 5 = -6
\][/tex]
Next, calculate the difference in the [tex]\( x \)[/tex]-coordinates:
[tex]\[
x_2 - x_1 = 6 - (-3) = 6 + 3 = 9
\][/tex]
Now, use these differences to find the slope:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6}{9} = -\frac{2}{3}
\][/tex]
Thus, the slope of the line containing the points [tex]\((-3, 5)\)[/tex] and [tex]\((6, -1)\)[/tex] is [tex]\(-\frac{2}{3}\)[/tex].
Therefore, the correct answer is:
B. [tex]\(-\frac{2}{3}\)[/tex]
