Module 2 - Lines

Module 2 - Answers

Lesson 1

Answer 1

2.1.1 Press

y = 3 when x = 2

Answer 2

2.1.2 The Viewing Window values of the ZSquare window in this example are approximately [-15, 15, 1] x [-10, 10, 1].

Lesson 2

Answer 1

2.2.1 Med-Med yields approximately y = -1441x + 14,199 as compared with the linear regression equation y = -1478x + 13,906, but they are slightly different from each other. Both equations are approximate linear models of the data but they vary slightly.

Lesson 3

Answer 1

2.3.1 The slope tells you that the value of the car decreases by about 1478 dollars each year.

The y-intercept tells you the linear regression model predicts that the price of a new car, at age x = 0, is about 13,906 dollars.

Answer 2

2.3.2 The slope is 5632 dollars per year, which indicates that the value of an average house is increasing at the rate of about 5632 dollars each year. The y-intercept is 14,760 dollars, which represents the value of an average home in 1970.

Answer 3

2.3.3 The slope is 58 dollars per square foot. This implies that each square foot of a home adds about $58 to the value of the house. Or in other words, each additional square foot in the size of a home increases the value by $58.

The y-intercept is $19,893, which represents the value of the property if there is no structure, i.e., x = 0 square feet. That is, the lot without a house is worth just under $20,000.

Answer 4

2.3.4 Carl runs with a velocity of approximately 10.7 meters/sec and Ray's velocity is about 8.1 meters/sec. Ray's equation implies that he was 10 meters from the starting line at the beginning of the race and so he had a head start of 10 meters. Carl passed Ray a little under 4 seconds after they started when they were about 40 meters from the starting line. Carl wins the race.

Self Test

Answer 1

Point-slope forms: or

Slope-intercept form:

Answer 2

Point-slope form:

Slope-intercept form:

Answer 3

The following window was obtained by pressing 6:Standard followed by 5:Zsquare.

Answer 4

[0.986, 10.846, 1] x [-17, 117, 10]

Answer 5

y = 10.7x – 8.1

Answer 6

Carl's velocity for the race was approximately 10.7 meters per second. The model implies that Carl started the race about 8.1 meters behind the starting line, but he certainly must have started at or very near the line, and the error in the model is required to produce the best fit over the entire data set.