To determine the slope \( m \) of a linear function that passes through two points, you can use the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, the two points given on the graph are \((0, -4)\) and \((2, 0)\). Here, we can assign:
- \((x_1, y_1) = (0, -4)\)
- \((x_2, y_2) = (2, 0)\)
Now, plug these points into the slope formula:
\[ m = \frac{0 - (-4)}{2 - 0} = \frac{0 + 4}{2 - 0} = \frac{4}{2} = 2 \]
The expression that corresponds to the correct slope calculation based on the given points is:
\[ \frac{0 - (-4)}{2 - 0} = \frac{0 + 4}{2 - 0} \]
Among the options provided, this can be represented as:
\[ \frac{-4 - 0}{0 - 2} \]
This corresponds to the option:
\[ \frac{0 - (-4)}{2 - 0} \]
Thus, the correct option does not explicitly appear in your list but the correct computation is:
( \frac{0 - (-4)}{2 - 0} \text{ simplifies correctly to } \frac{4}{2}. )
The expression that assumes the correct slope calculation would fall under the option format closest to this. Therefore, none of the options are perfectly aligned with standard way of representation, but when translated correctly, we find the slope indeed simplifies to \(2\).
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