To find the slope of the line given the points \((0, 0)\), \((2, -2)\), \((4, -4)\), and \((6, -6)\), we can use the formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's calculate the slope using the first two points \((0, 0)\) and \((2, -2)\):
\[ m = \frac{-2 - 0}{2 - 0} = \frac{-2}{2} = -1 \]
We can verify this using another pair, such as \((2, -2)\) and \((4, -4)\):
\[ m = \frac{-4 - (-2)}{4 - 2} = \frac{-4 + 2}{2} = \frac{-2}{2} = -1 \]
Finally, we can also check \((4, -4)\) and \((6, -6)\):
\[ m = \frac{-6 - (-4)}{6 - 4} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \]
In all cases, the slope is \(-1\).
So the answer is:
A. -1