To determine the slope of the line that contains the points \((9, -4)\) and \((1, -5)\), we will use the slope formula, which is given by:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, \((x_1, y_1) = (9, -4)\) and \((x_2, y_2) = (1, -5)\).
Let's plug in the coordinates into the formula:
1. Calculate the difference in the \(y\)-coordinates:
[tex]\[ y_2 - y_1 = -5 - (-4) = -5 + 4 = -1 \][/tex]
2. Calculate the difference in the \(x\)-coordinates:
[tex]\[ x_2 - x_1 = 1 - 9 = -8 \][/tex]
Now, divide the difference in the \(y\)-coordinates by the difference in the \(x\)-coordinates to find the slope:
[tex]\[ \text{slope} = \frac{-1}{-8} = \frac{1}{8} \][/tex]
Therefore, the slope of the line is \(\frac{1}{8}\).
The correct answer is:
D. [tex]\(\frac{1}{8}\)[/tex]
