To determine the slope of the line using the coordinates given, we can calculate the slope between two points. The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's take the first two points from your list:
- Point 1: (4, 8)
- Point 2: (2, 4)
Using the formula:
- \( x_1 = 4, y_1 = 8 \)
- \( x_2 = 2, y_2 = 4 \)
Now plug in the values:
\[ m = \frac{4 - 8}{2 - 4} = \frac{-4}{-2} = 2 \]
Now let's check the slope between points (3, 6) and (1, 2):
- Point 1: (3, 6)
- Point 2: (1, 2)
Applying the same formula:
- \( x_1 = 3, y_1 = 6 \)
- \( x_2 = 1, y_2 = 2 \)
Now plug in:
\[ m = \frac{2 - 6}{1 - 3} = \frac{-4}{-2} = 2 \]
Finally, we can check from another set, (2, 4) and (0, 0):
- Point 1: (2, 4)
- Point 2: (0, 0)
Using the same formula:
- \( x_1 = 2, y_1 = 4 \)
- \( x_2 = 0, y_2 = 0 \)
Now plug in:
\[ m = \frac{0 - 4}{0 - 2} = \frac{-4}{-2} = 2 \]
In all cases, the slope calculated is the same. Thus, the slope of the line is:
\[ \text{slope} = 2 \]
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