To determine the slope of the line passing through the points [tex]\((4, -2)\)[/tex] and [tex]\((-3, -9)\)[/tex], we can use the formula for the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given the points [tex]\((4, -2)\)[/tex] and [tex]\((-3, -9)\)[/tex]:
1. Assign the coordinates:
[tex]\[
(x_1, y_1) = (4, -2) \\
(x_2, y_2) = (-3, -9)
\][/tex]
2. Substitute the coordinates into the slope formula:
[tex]\[
m = \frac{-9 - (-2)}{-3 - 4}
\][/tex]
3. Simplify the numerator and the denominator:
[tex]\[
m = \frac{-9 + 2}{-3 - 4}
\][/tex]
[tex]\[
m = \frac{-7}{-7}
\][/tex]
4. Simplify the fraction:
[tex]\[
m = 1.0
\][/tex]
Therefore, the slope of the line passing through the points [tex]\((4, -2)\)[/tex] and [tex]\((-3, -9)\)[/tex] is [tex]\(1.0\)[/tex].
So, the correct choice is:
A. The slope is [tex]\(1.0\)[/tex].
