Question

Answer the following questions about the problem above. Write in complete sentences to get full credit.
1. What is the slope for section "d" of Mrs. Washington's commute.
2. What does it mean that the slope is negative in context of the problem?
3. Why are the slopes different over different intervals?
4. How long does it take Mrs. Washington to get home? How did you know this?

Answer 1

Note: Since you missed to add the image, so after a little research, I was able to find the image related to this question, which hopefully serves the purpose to clear your concept. The image is attached below.

Step-by-step explanation:

Part 1) What is the slope for section "d" of Mrs. Washington's commute

Calculating the slope for section "d" of Mrs. Washington's commute:

Slope of the section d  $=\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$\frac{6 - 0}{32 - 20}=\frac{1}{2}=0.5$

Part 2) What does it mean that the slope is negative in context of the problem?

The slope is being negative as it is moving downward from the left. In negative slop, the value of x increase, while the vale of y decreases. In positive slop, the value of both x and y increases.

Part 3) Why are the slopes different over different intervals?

Slopes are different at different intervals as the distance covered in time taken for each part of the given journey are different, also the speed is not the same for each interval.

As the speed can be calculated as

$Speed\:=\:\frac{distance}{time}\:$

Distance = $y_{2} -y_{1}$ = $20 - 15 = 5$

Time = $x_{2} -x_{1}$= $8 - 0 = 8$

Speed = $\frac{5}{8}=0.625$

Therefore, the speed in the part 1 is $0.625$ $ms^{-1}$

Part 4) How long does it take Mrs. Washington to get home? How did you know this?

It is clear from the graph that does take 32 minutes to her to get home.  

We can observe it from the graph that it represents the total time taken across the entire journey.

Keywords: slope, speed, time

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