Like any slope we can interpret this as a rate of

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Unformatted text preview: t is 24◦ F; at 10 AM, it is 32◦ F. 1. Find the slope of the line containing the points (6, 24) and (10, 32). 2. Interpret your answer to the first part in terms of temperature and time. 3. Predict the temperature at noon. Solution. 1. For the slope, we have m = 32−24 10−6 = 8 4 = 2. 2. Since the values in the numerator correspond to the temperatures in ◦ F, and the values in 2 2◦ F the denominator correspond to time in hours, we can interpret the slope as 2 = = , 1 1 hour ◦ F per hour. Since the slope is positive, we know this corresponds to an increasing line. or 2 Hence, the temperature is increasing at a rate of 2◦ F per hour. 3. Noon is two hours after 10 AM. Assuming a temperature increase of 2◦ F per hour, in two hours the temperature should rise 4◦ F. Since the temperature at 10 AM is 32◦ F, we would expect the temperature at noon to be 32 + 4 = 36◦ F. Now it may well happen that in the previous scenario, at noon the temperature is only 33◦ F. This doesn’t mean our calculations a...
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