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. For this to be a linear situation, we must assume that Marisa is walking a straight path so that the time needed to cover a distance is constant.

B. The equation of the line is given as:

y = m x + b

where in this case y is the distance, m is the slope or the time it takes for each block, x is the time, and b is the y intercept or the initial position 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 means that the distance between Marisa and Sanjay’s home is decreasing by time. It further means that there is a decrease in 0.67 blocks per minute.

D. y = - 0.67 x + b

The initial point of Marisa is at 12 blocks away from Sanjay’s home, hence b = 12.

Finding for time x when distance is 0 (y = 0):

0 = -0.67 x + 12

x = 17.9 minutes

Hence it takes around 17.9 minutes to reach Sanjay’s home.