To determine the rate of the graph you described, we can identify the slope of the line formed by the points (1, -1), (2, -2), (3, -3), (4, -4), (5, -5), and (6, -6).
The slope (rate) of a line can be calculated using the formula:
\[ \text{slope} = \frac{\text{change in } y}{\text{change in } x} \]
From your description, as \( x \) increases from 1 to 6, \( y \) decreases from -1 to -6.
- For the first pair of values, when \( x = 1 \) and \( y = -1 \), and when \( x = 6 \) and \( y = -6 \):
- Change in \( y \) = \( -6 - (-1) = -6 + 1 = -5 \)
- Change in \( x \) = \( 6 - 1 = 5 \)
Using the slope formula:
\[ \text{slope} = \frac{-5}{5} = -1 \]
So the rate of the graph (slope) is -1. This indicates that for every 1 unit increase in \( x \), \( y \) decreases by 1 unit.
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