What is the slope of the line that passes through the points (7, -4) and (11, -4)? Write your answer in simplest form.
The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is determined by the ratio of the vertical change to the horizontal change between them. Given the points \((7, -4)\) and \((11, -4)\), we identify \(x_1 = 7\), \(y_1 = -4\), \(x_2 = 11\), and \(y_2 = -4\). The slope formula is defined as \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
We substitute the coordinates of our points into the slope formula:
\[m = \frac{-4 - (-4)}{11 - 7}\]
Next, we simplify the numerator and the denominator:
\[m = \frac{-4 + 4}{4}\]
\[m = \frac{0}{4}\]
Finally, we perform the division:
\[m = 0\]
Since the slope is \(0\), this indicates that the line passing through \((7, -4)\) and \((11, -4)\) is a horizontal line. The simplest form of this slope is \(\boxed{0}\).
In real-world applications, a slope of 0 represents a horizontal path or state. For example, if you are walking along a perfectly level floor or tracking an object's elevation over time where the altitude remains constant, the rate of change (the slope) is zero. This tells you that no matter how far you travel along the horizontal axis, your vertical position remains unchanged, which is vital for engineering level surfaces or analyzing constant data trends.