To determine whether the relationship between time (in hours) and temperature (in Celsius) is linear, nonlinear, a function, or not a function, let's analyze the data:
The provided data points are:
- (3, 5)
- (6, 0)
- (9, -5)
- (12, -10)
Checking if it is a function:
A relation is a function if each input (time) is associated with exactly one output (temperature). Here, each time value maps to one unique temperature value. Therefore, this relation is a function.
Checking for linearity:
To determine whether the relation is linear, we can check if the temperature changes by a constant amount for equal changes in time (i.e., check if the slope between the points is constant).
- Calculate the slope between points:
-
From (3, 5) to (6, 0): \[ \text{slope} = \frac{0 - 5}{6 - 3} = \frac{-5}{3} \]
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From (6, 0) to (9, -5): \[ \text{slope} = \frac{-5 - 0}{9 - 6} = \frac{-5}{3} \]
-
From (9, -5) to (12, -10): \[ \text{slope} = \frac{-10 - (-5)}{12 - 9} = \frac{-5}{3} \]
-
Since the slope between each pair of points is the same (-5/3), the relationship is linear.
Conclusion:
The relationship between time and temperature is a linear function.
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