To find the slope of the line passing through the points [tex]\((7,6)\)[/tex] and [tex]\((-2, -9)\)[/tex], we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given the points [tex]\((x_1, y_1) = (7, 6)\)[/tex] and [tex]\((x_2, y_2) = (-2, -9)\)[/tex], we can substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{-9 - 6}{-2 - 7}
\][/tex]
First, simplify the numerator and the denominator:
[tex]\[
-9 - 6 = -15
\][/tex]
[tex]\[
-2 - 7 = -9
\][/tex]
Now, we have:
[tex]\[
\text{slope} = \frac{-15}{-9}
\][/tex]
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
\text{slope} = \frac{-15 \div 3}{-9 \div 3} = \frac{-5}{-3} = \frac{5}{3}
\][/tex]
So, the slope of the line passing through the points [tex]\((7, 6)\)[/tex] and [tex]\((-2, -9)\)[/tex] is:
[tex]\[
\boxed{\frac{5}{3}}
\][/tex]
