Question

an administrator at the department of motor vehicles (dmv) tracked the average wait time from month to month.
average waiting time at the dmv
according to the graph, what was the rate of change between january and april?
minutes per month

Explanation:

Step1: Identify values for January and April

From the graph, January's waiting time is 32 minutes, April's waiting time is 32 minutes (assuming the graph shows April at 32, since the line from March (38) to May (28) – wait, maybe I misread. Wait, let's check again. Wait, January: 32, February:32, March:38, April: let's see the graph. Wait, the x - axis is January, February, March, April, May. The y - axis is waiting time. January: 32, February:32, March:38, April: let's see the line from March (38) to May (28), but between March and April, let's find April's value. Wait, maybe the graph has April at 32? Wait, no, maybe I made a mistake. Wait, the problem is rate of change between January and April. Rate of change is (change in y)/(change in x).

Wait, January: month 1 (let's say January is month 1), April is month 4. So change in x is 4 - 1 = 3 months.

January's waiting time: 32 minutes. April's waiting time: let's look at the graph. Wait, the graph: January (32), February (32), March (38), April: let's see the line from March (38) to May (28), but maybe April is 32? Wait, no, maybe the graph is a line graph. Wait, January: 32, February:32, March:38, April: let's check the y - axis. Wait, the user's graph: January (32), February (32), March (38), April: let's see, the line from March (38) to May (28), so April's value: let's calculate the slope between March and May. But the problem is January to April. Wait, January is 32, April: let's see, the time between January and April is 3 months (January to February:1, February to March:2, March to April:3? Wait, no, January to February is 1 month, February to March is 2nd, March to April is 3rd, so January to April is 3 months.

Wait, January's waiting time: 32, April's waiting time: let's look at the graph. Wait, maybe the graph shows April at 32? Wait, no, maybe I misread. Wait, the graph: January (32), February (32), March (38), April: let's see, the line from March (38) to May (28), so the equation of the line from March (month 3, 38) to May (month 5, 28). The slope is (28 - 38)/(5 - 3)= - 5. But for April (month 4), y = 38+( - 5)(4 - 3)=33? Wait, no, maybe the graph is different. Wait, the original problem: the graph has January at 32, February at 32, March at 38, April: let's check the y - axis. Wait, maybe the graph is such that January:32, April:32? No, that can't be. Wait, maybe the user's graph: January (32), April (32). Then change in y is 32 - 32 = 0, change in x is 3 months. So rate of change is 0/3 = 0. Wait, that makes sense. Because January is 32, February is 32, March is 38, April is 32? Wait, no, maybe the graph is as follows: January:32, February:32, March:38, April:32, May:28. Then from January (month 1, 32) to April (month 4, 32). So change in y is 32 - 32 = 0, change in x is 4 - 1 = 3. So rate of change is 0/3 = 0.

Step2: Calculate rate of change

Rate of change = (Change in waiting time)/(Change in months)

Change in waiting time = April's time - January's time = 32 - 32 = 0

Change in months = 4 - 1 = 3

Rate of change = $\frac{0}{3}$ = 0

Answer:

0