To determine the slope of the line that passes through the points [tex]\((3, 7)\)[/tex] and [tex]\((4, -8)\)[/tex], we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first point and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point. Plugging in the values from the given points:
[tex]\[
x_1 = 3, \quad y_1 = 7, \quad x_2 = 4, \quad y_2 = -8
\][/tex]
Substituting these values into the slope formula gives:
[tex]\[
m = \frac{-8 - 7}{4 - 3}
\][/tex]
Now, calculate the differences in the numerator and the denominator:
[tex]\[
-8 - 7 = -15
\][/tex]
[tex]\[
4 - 3 = 1
\][/tex]
So the slope [tex]\(m\)[/tex] is:
[tex]\[
m = \frac{-15}{1} = -15
\][/tex]
Therefore, the slope of the line joining the points [tex]\((3, 7)\)[/tex] and [tex]\((4, -8)\)[/tex] is:
[tex]\[
\boxed{-15}
\][/tex]
