To find the slope of the line containing the pair of points [tex]\((8, 9)\)[/tex] and [tex]\((10, -7)\)[/tex], follow these steps:
1. Identify the coordinates of the points:
- Point [tex]\((x_1, y_1)\)[/tex] is [tex]\((8, 9)\)[/tex]
- Point [tex]\((x_2, y_2)\)[/tex] is [tex]\((10, -7)\)[/tex]
2. Calculate the change in [tex]\(x\)[/tex] (denoted as [tex]\(\Delta x\)[/tex]):
[tex]\[
\Delta x = x_2 - x_1
\][/tex]
Substituting the given values:
[tex]\[
\Delta x = 10 - 8 = 2
\][/tex]
3. Calculate the change in [tex]\(y\)[/tex] (denoted as [tex]\(\Delta y\)[/tex]):
[tex]\[
\Delta y = y_2 - y_1
\][/tex]
Substituting the given values:
[tex]\[
\Delta y = -7 - 9 = -16
\][/tex]
4. Calculate the slope of the line:
The slope [tex]\(m\)[/tex] is given by the ratio of the change in [tex]\(y\)[/tex] to the change in [tex]\(x\)[/tex]:
[tex]\[
m = \frac{\Delta y}{\Delta x}
\][/tex]
Substituting the values we calculated:
[tex]\[
m = \frac{-16}{2} = -8.0
\][/tex]
In summary:
- The change in [tex]\(x\)[/tex] ([tex]\(\Delta x\)[/tex]) is [tex]\(2\)[/tex].
- The change in [tex]\(y\)[/tex] ([tex]\(\Delta y\)[/tex]) is [tex]\(-16\)[/tex].
- The slope of the line is [tex]\(-8.0\)[/tex].
