To find the slope of the line through the given points [tex]\((-8, 6)\)[/tex] and [tex]\((4, 6)\)[/tex], we'll follow these steps meticulously.
### Step 1: Understand the Coordinates
We have two points:
- [tex]\( (x1, y1) = (-8, 6) \)[/tex]
- [tex]\( (x2, y2) = (4, 6) \)[/tex]
### Step 2: Calculate the Rise and Run
- Rise: This is the change in [tex]\(y\)[/tex]-coordinates.
[tex]\[
\text{Rise} = y2 - y1 = 6 - 6 = 0
\][/tex]
- Run: This is the change in [tex]\(x\)[/tex]-coordinates.
[tex]\[
\text{Run} = x2 - x1 = 4 - (-8) = 4 + 8 = 12
\][/tex]
### Step 3: Calculate the Slope
The slope [tex]\(m\)[/tex] of a line is given by the formula:
[tex]\[
m = \frac{\text{rise}}{\text{run}}
\][/tex]
Plugging in our values:
[tex]\[
m = \frac{0}{12} = 0
\][/tex]
### Conclusion
The slope [tex]\(m\)[/tex] of the line through the points [tex]\((-8, 6)\)[/tex] and [tex]\((4, 6)\)[/tex] is [tex]\(0\)[/tex]. This indicates a horizontal line with zero slope.
So the correct answer is:
- [tex]\(\boxed{0}\)[/tex]
The computed slope confirms that the multiple choice option [tex]\(m = 0\)[/tex] is the correct answer.
