What is the slope of the line that passes through the points (9,-5) and (1,-1)? Write your answer in simplest form.
To find the slope of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula:
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
Here, our points are \((x_1, y_1) = (9, -5)\) and \((x_2, y_2) = (1, -1)\).
Substitute the given coordinates into the slope formula:
\[m = \frac{-1 - (-5)}{1 - 9}\]
Simplify the numerator:
\[-1 - (-5) = -1 + 5 = 4\]
Simplify the denominator:
\[1 - 9 = -8\]
So, the slope is:
\[m = \frac{4}{-8}\]
Finally, reduce the fraction \(\frac{4}{-8}\) to its simplest form:
\[m = -\frac{4}{8} = -\frac{1}{2}\]
The slope of the line passing through the points \((9, -5)\) and \((1, -1)\) is \(\boxed{-\frac{1}{2}}\).
In navigation, slope can represent the grade or steepness of a road. If a road rises or falls a certain amount over a horizontal distance, the ratio of the vertical change (rise) to the horizontal change (run) tells you how steep the climb will be. For example, if a road drops 1 unit of elevation for every 2 units of horizontal distance, the slope of that road is \(m = -\frac{1}{2}\).