To find the slope of a line determined by two points, you can use the formula for the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the first two points \((0, 0)\) and \((2, -2)\):
- \(x_1 = 0\), \(y_1 = 0\)
- \(x_2 = 2\), \(y_2 = -2\)
Plugging in the values:
\[ m = \frac{-2 - 0}{2 - 0} = \frac{-2}{2} = -1 \]
Now, let's check with another pair of points, for example, the second point \((2, -2)\) and the third point \((4, -4)\):
- \(x_1 = 2\), \(y_1 = -2\)
- \(x_2 = 4\), \(y_2 = -4\)
Calculating the slope:
\[ m = \frac{-4 - (-2)}{4 - 2} = \frac{-4 + 2}{2} = \frac{-2}{2} = -1 \]
Finally, checking the slope between the third point \((4, -4)\) and the fourth point \((6, -6)\):
- \(x_1 = 4\), \(y_1 = -4\)
- \(x_2 = 6\), \(y_2 = -6\)
Calculating the slope:
\[ m = \frac{-6 - (-4)}{6 - 4} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \]
Thus, the slope of the line connecting the points (0, 0), (2, -2), (4, -4), and (6, -6) is consistently \( -1 \).