Question

zendaya left her house at time zero and drove for 3 minutes to the store, at a speed of 3 blocks per minute. then she stopped and went into the store for 4 minutes. from there, she drove in the same direction at a speed of 2 blocks per minute until she got to the bank, which is 6 blocks away from the store. she stopped at the bank for 2 minutes. then she drove home at a speed of 3 blocks every minute. make a graph of showing the number of blocks away from home that zendaya is 2 minutes after she leaves her house, until she gets back home.
click twice to plot a segment.
click a segment to delete it.

Explanation:

Step1: Calculate distance to first store

Distance = Speed × Time = $3 \text{ blocks/min} \times 3 \text{ min} = 9 \text{ blocks}$
This segment goes from $(0,0)$ to $(3,9)$.

Step2: Plot store stop (4 mins)

Time increases from 3 to $3+4=7$ minutes, distance stays 9 blocks.
This segment goes from $(3,9)$ to $(7,9)$.

Step3: Calculate distance to bank

New distance = $9 + (2 \text{ blocks/min} \times 3 \text{ min}) = 9+6=15 \text{ blocks}$
Time increases from 7 to $7+3=10$ minutes.
This segment goes from $(7,9)$ to $(10,15)$.

Step4: Plot bank stop (2 mins)

Time increases from 10 to $10+2=12$ minutes, distance stays 15 blocks.
This segment goes from $(10,15)$ to $(12,15)$.

Step5: Calculate time to drive home

Time = $\frac{\text{Total Distance}}{\text{Speed}} = \frac{15 \text{ blocks}}{3 \text{ blocks/min}} = 5 \text{ minutes}$
Time increases from 12 to $12+5=17$ minutes, distance drops to 0.
This segment goes from $(12,15)$ to $(17,0)$.

Answer:

The graph consists of 5 connected segments with endpoints:

1. $(0, 0)$ to $(3, 9)$
2. $(3, 9)$ to $(7, 9)$
3. $(7, 9)$ to $(10, 15)$
4. $(10, 15)$ to $(12, 15)$
5. $(12, 15)$ to $(17, 0)$