Question

at what rate did the temperature rise from 9 a.m. to 1 p.m.?
answer
1°f every 2 hours 1°f every 4 hours
2°f every 1 hour 4°f every 1 hour

Explanation:

Step1: Identify temperature at 9 am and 1 pm

From the graph, at 9 am (3 hours after 6 am), the temperature is 56°F (assuming the point between 6 am (50°F) and noon (let's check: at 6 am it's 50, then a point at maybe 9 am? Wait, the x - axis: 6 am, then noon (12), 6 pm, midnight. Let's re - examine. At 6 am, temperature is 50°F. Then at 9 am (3 hours later), let's see the first segment: from 6 am (50°F) to a point (maybe 9 am) with temperature, then to noon. Wait, maybe the points: 6 am: 50, then a point at, say, 9 am: 56? Wait, no, the problem is about 9 am to 1 pm. 9 am to 1 pm is 4 hours. Let's find temperature at 9 am and 1 pm. Let's assume at 9 am, temperature is 56°F (from the graph: 6 am is 50, then a point at, maybe, 9 am (3 hours after 6 am) with y = 56, and at 1 pm (5 hours after 6 am? Wait, 6 am to 1 pm is 7 hours? No, 9 am to 1 pm is 4 hours (13 - 9 = 4). Wait, maybe the graph: at noon (12 pm) the temperature is 72°F? Wait, the peak is between noon and 6 pm. Wait, maybe the first segment: from 6 am (50°F) to a point at, say, 9 am (3 hours later) with temperature, then to noon (12 pm) with temperature. Wait, maybe the correct way: rate of change is (change in temperature)/(change in time). Let's find temperature at 9 am and 1 pm. Let's assume at 9 am, temperature is 56°F (since from 6 am (50) to a point, then to noon (12 pm) where temperature is 72? Wait, no, the graph has a steep rise to noon. Wait, maybe the temperature at 9 am is 56, and at 1 pm is 72? Wait, 9 am to 1 pm is 4 hours. Change in temperature: 72 - 56 = 16? No, that can't be. Wait, maybe I misread. Wait, the y - axis: 50, 55, 60, 65, 70, 75. At 6 am: 50. Then a point at, say, 9 am (3 hours after 6 am) with y = 56? Then at noon (6 hours after 6 am) y = 72? Then from 9 am (3h) to 1 pm (7h, since 6 am + 7h = 1 pm), time difference is 4h (7 - 3 = 4). Temperature at 9 am: 56, at 1 pm: 72? Then change in temperature: 72 - 56 = 16. Rate: 16/4 = 4°F per hour? Wait, no, maybe the temperature at 9 am is 56 and at 1 pm is 72? Wait, 72 - 56 = 16, over 4 hours: 16/4 = 4. So rate is 4°F per hour.

Step2: Calculate rate of change

Rate of change (slope) is $\frac{\text{Change in Temperature}}{\text{Change in Time}}$. Change in time from 9 am to 1 pm: 1 pm - 9 am = 4 hours. Let's find change in temperature. From the graph, assume at 9 am, temperature is 56°F, and at 1 pm, temperature is 72°F (since the peak is around noon - 6 pm, and 1 pm is before the peak? Wait, no, the peak is between noon and 6 pm. Wait, maybe the temperature at 9 am is 56, and at 1 pm is 72. Then $\Delta T=72 - 56 = 16$, $\Delta t = 4$ hours. So rate is $\frac{16}{4}=4$°F per hour.

Answer:

4°F every 1 hour