To find the slope of the line passing through the points \((4, -6)\) and \((7, -6)\), we will follow these steps:
1. Identify the coordinates:
- The first point \((x_1, y_1)\) is \((4, -6)\).
- The second point \((x_2, y_2)\) is \((7, -6)\).
2. Calculate the change in \(x\) and \(y\):
- The change in \(x\) (Δx) is \(x_2 - x_1\).
[tex]\[
\Delta x = 7 - 4 = 3
\][/tex]
- The change in \(y\) (Δy) is \(y_2 - y_1\).
[tex]\[
\Delta y = -6 - (-6) = -6 + 6 = 0
\][/tex]
3. Calculate the slope:
- The slope \(m\) is given by the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x}
\][/tex]
- Plugging in the values we calculated:
[tex]\[
m = \frac{0}{3} = 0
\][/tex]
4. Interpret the slope:
- The slope of \(0\) indicates that the line is horizontal.
So, the slope of the line passing through the points [tex]\((4, -6)\)[/tex] and [tex]\((7, -6)\)[/tex] is [tex]\(\boxed{0}\)[/tex].
