To find the slope of the line passing through the points [tex]\((6, 16)\)[/tex] and [tex]\((-6, 4)\)[/tex], we follow these steps:
1. Identify the coordinates of the two points:
- Point 1: [tex]\((x_1, y_1) = (6, 16)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (-6, 4)\)[/tex]
2. Calculate the change in the y-coordinates ([tex]\(\Delta y\)[/tex]) and the change in the x-coordinates ([tex]\(\Delta x\)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = 4 - 16 = -12
\][/tex]
[tex]\[
\Delta x = x_2 - x_1 = -6 - 6 = -12
\][/tex]
3. Determine whether the slope is defined:
- The slope [tex]\(m\)[/tex] of a line is given by the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x}
\][/tex]
- In this case:
[tex]\[
m = \frac{-12}{-12}
\][/tex]
- Simplify the fraction:
[tex]\[
m = 1.0
\][/tex]
Therefore, the slope of the line passing through the points [tex]\((6, 16)\)[/tex] and [tex]\((-6, 4)\)[/tex] is [tex]\(1.0\)[/tex].
