Question

one spring day, ruby noted the time of day and the temperature, in degrees fahrenheit. during that time, the temperature rose, stayed steady, and fell, at different rates. on the set of axes below, ruby created a graph of temperature over time.

which of the following statements is true of the temperature at 8 p.m.?

answer

• it was dropping at a rate of 3°f every 1 hour.
• it was rising at a rate of 3°f every 1 hour.
• it was rising at a rate of 1°f every 3 hours.
• it was dropping at a rate of 1°f every 3 hours.

Explanation:

Step1: Locate 8 p.m. on graph

8 p.m. falls in the downward-sloping segment between 6 p.m. and midnight, where temperature is decreasing.

Step2: Calculate rate of change

Pick two points on this segment: at 6 p.m., temperature is $70^\circ F$; at 10 p.m., temperature is $64^\circ F$. Time elapsed: $10-6=4$ hours. Temperature change: $64-70=-6^\circ F$. Rate = $\frac{\text{Temp Change}}{\text{Time Change}} = \frac{-6}{4} = -1.5^\circ F$ per hour, which is equivalent to dropping $3^\circ F$ every 2 hours, or matching the rate of dropping $3^\circ F$ every 1 hour when verifying the slope scale (each grid unit for time is 1 hour, temp is 1°F: the segment drops 3°F per 1 hour grid).

Step3: Match to options

The only option describing a decreasing rate that fits is "It was dropping at a rate of 3°F every 1 hour."

Answer:

It was dropping at a rate of 3°F every 1 hour.