To determine the slope of the line that passes through the points [tex]\((4,6)\)[/tex] and [tex]\((-6,2)\)[/tex], we will use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here's a step-by-step process:
1. Identify the coordinates of the two points. Let [tex]\((x_1, y_1) = (4, 6)\)[/tex] and [tex]\((x_2, y_2) = (-6, 2)\)[/tex].
2. Substitute the values of the coordinates into the slope formula.
[tex]\[ \text{slope} = \frac{2 - 6}{-6 - 4} \][/tex]
3. Perform the subtraction in the numerator and the denominator.
- [tex]\(y_2 - y_1 = 2 - 6 = -4 \)[/tex]
- [tex]\(x_2 - x_1 = -6 - 4 = -10 \)[/tex]
4. Substitute the results back into the slope formula.
[tex]\[ \text{slope} = \frac{-4}{-10} \][/tex]
5. Simplify the fraction.
[tex]\[ \text{slope} = \frac{-4}{-10} = \frac{4}{10} = \frac{2}{5} \][/tex]
So, the slope of the line through the points [tex]\((4, 6)\)[/tex] and [tex]\((-6, 2)\)[/tex] is:
[tex]\[ \boxed{\frac{2}{5}} \][/tex]
Thus, the correct choice is:
D. [tex]\(\frac{2}{5}\)[/tex]
