To find the slope of the line passing through the points [tex]\((-6, -5)\)[/tex] and [tex]\((4, 1)\)[/tex], we use the slope formula. The formula for the slope [tex]\(m\)[/tex] between 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]
Substitute the coordinates of the points [tex]\((-6, -5)\)[/tex] and [tex]\((4, 1)\)[/tex] into the formula:
[tex]\[ x_1 = -6, \; y_1 = -5, \; x_2 = 4, \; y_2 = 1 \][/tex]
Now calculate the differences in the y-coordinates and x-coordinates:
[tex]\[ y_2 - y_1 = 1 - (-5) = 1 + 5 = 6 \][/tex]
[tex]\[ x_2 - x_1 = 4 - (-6) = 4 + 6 = 10 \][/tex]
Plug these values into the slope formula:
[tex]\[ m = \frac{6}{10} \][/tex]
Simplify the fraction:
[tex]\[ m = \frac{3}{5} \][/tex]
By converting [tex]\( \frac{3}{5} \)[/tex] into decimal form, we get:
[tex]\[ m = 0.6 \][/tex]
Therefore, the slope of the line passing through the points [tex]\((-6, -5)\)[/tex] and [tex]\((4, 1)\)[/tex] is [tex]\(0.6\)[/tex]. Since none of the provided multiple-choice options are in the form of the correct slope, it seems there is no accurate answer in the choices given. The correct value for the slope of this line is [tex]\( \boxed{0.6} \)[/tex].
