Question

daily commutes
social scientists surveyed workers about their daily commutes to work. the data are shown in the table.

average commute time
minutes to work, y	22.3	24.0	24.5	25.3

question: 3
which equation models the line of best fit for the data?
a. $y = -3.0x + 22.3$
b. $y = 3.0x + 22.3$
c. $y = -0.30x + 22.4$
d. $y = 0.30x + 22.4$

question: 4
to the nearest tenth, what was the predicted average commute time in minutes for workers in 2008, 3 years after 2005?
minutes

Explanation:

Question 3

Step1: Analyze the trend

As \( x \) (years since 2005) increases, \( y \) (minutes to work) also increases. So the slope should be positive, eliminating options A and C.

Step2: Check the slope magnitude

Let's calculate the approximate slope. Using two points, e.g., \( (0, 22.3) \) and \( (5, 24.0) \). The slope \( m=\frac{24.0 - 22.3}{5 - 0}=\frac{1.7}{5}=0.34 \), close to 0.30. Option B has a slope of 3.0, which is too large. So the correct equation is \( y = 0.30x + 22.4 \) (option D).

Step1: Use the line of best fit

From Question 3, the line of best fit is \( y = 0.30x + 22.4 \). For 2008, \( x = 3 \) (3 years since 2005).

Step2: Substitute \( x = 3 \) into the equation

\( y=0.30(3)+22.4=0.9 + 22.4 = 23.3 \).

Answer:

D. \( y = 0.30x + 22.4 \)

Question 4