To find the slope of the line that contains the given points [tex]\((39, 36)\)[/tex], [tex]\((40, 29)\)[/tex], [tex]\((41, 22)\)[/tex], and [tex]\((42, 15)\)[/tex], we need to use the formula for the slope [tex]\((m)\)[/tex] between any 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]
We will use the first point [tex]\((39, 36)\)[/tex] and the last point [tex]\((42, 15)\)[/tex] to calculate the slope.
1. Determine the change in [tex]\(x\)[/tex]:
[tex]\[
\Delta x = x_2 - x_1 = 42 - 39 = 3
\][/tex]
2. Determine the change in [tex]\(y\)[/tex]:
[tex]\[
\Delta y = y_2 - y_1 = 15 - 36 = -21
\][/tex]
3. Now, calculate the slope:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{-21}{3} = -7.0
\][/tex]
Therefore, the slope of the line that contains the given points is:
[tex]\[
\boxed{-7.0}
\][/tex]
