To determine the correct description for the given set of coordinates, we first need to analyze the points and check two main criteria: whether the relationship is linear and whether it is a function.
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Check if it's a function: A relation is a function if each input (x-value) corresponds to exactly one output (y-value). The given points are:
- (-2, -7)
- (-1, -4)
- (0, -1)
- (1, 2)
- (2, 5)
All x-values are unique; therefore, this is a function.
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Check if it's linear: A linear relationship produces points that can be connected to form a straight line. To determine if the relationship is linear, we calculate the slopes between the points:
- Slope between (-2, -7) and (-1, -4): \[\text{slope} = \frac{-4 - (-7)}{-1 - (-2)} = \frac{3}{1} = 3\]
- Slope between (-1, -4) and (0, -1): \[\text{slope} = \frac{-1 - (-4)}{0 - (-1)} = \frac{3}{1} = 3\]
- Slope between (0, -1) and (1, 2): \[\text{slope} = \frac{2 - (-1)}{1 - (0)} = \frac{3}{1} = 3\]
- Slope between (1, 2) and (2, 5): \[\text{slope} = \frac{5 - 2}{2 - 1} = \frac{3}{1} = 3\]
Since the slope is consistent between all points, the relationship is linear.
Based on the analysis, the correct description for the given graph is: linear; function.