To find the slope of the line that passes through the given points [tex]\((6, -3)\)[/tex], [tex]\((-2, 1)\)[/tex], and [tex]\((-4, 2)\)[/tex], we will use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are any two points on the line.
Let's choose the points [tex]\((6, -3)\)[/tex] and [tex]\((-2, 1)\)[/tex]. Applying these points to the slope formula, we get:
[tex]\[
\text{slope} = \frac{1 - (-3)}{-2 - 6}
\][/tex]
First, simplify the numerator:
[tex]\[
1 - (-3) = 1 + 3 = 4
\][/tex]
Next, simplify the denominator:
[tex]\[
-2 - 6 = -8
\][/tex]
Now, substitute these simplified values back into the slope equation:
[tex]\[
\text{slope} = \frac{4}{-8}
\][/tex]
Simplify the fraction:
[tex]\[
\text{slope} = \frac{4}{-8} = -0.5
\][/tex]
Thus, the slope of the line passing through the given points is [tex]\(-0.5\)[/tex].
