Question

Marisa is walking from her home to her friend Sanjay's home. When she is 12 blocks away from Sanjay's home she looks at her watch. she looks again when she is 8 blocks away from Sanjay's home and finds that 6 minutes have passed?
A.what do you need to assume in order to treat this as a linear situation
B. identified the variables for the linear situation and identify two points on the line explain the meaning of the points in the in the context of the problem
C. find the slope of the line and describe what it means in the context of the problem
D. write an equation in point slope form for the situation and use it to find the number of minutes It takes to reach Sanjay's home. show your work

Answer 1

A. We must consider that Marisa is walking a straight trail so that the time required to cover a distance is persistent or constant.

 

B. The slope of the line is: y = m x + b

Where in this problem, y is the distance, m is the slope or the time it takes for each block, x is the time, and b would be the y intercept or the initial location of Marisa.

 

C. The slope m can be calculated using the formula:

m = (y2 – y1) / (x2 – x1)

m = (8 – 12) / (6 – 0)

m = -0.67

The negative sign is the space between Marisa and Sanjay’s home is declining by time. It further means that there is a cut in 0.67 blocks per minute.

 

D. y = - 0.67 x + b

The starting point of Marisa is at 12 blocks away from Sanjay’s home, therefore let b be 12.

Finding for time when distance is y = 0:

0 = -0.67 x + 12

x = 17.9 minutes

Therefore it takes approximately 17.9 minutes to go to Sanjay’s home.