Question

the table shows the maximum recommended viewing distances y, in feet, for an hdtv with screen size x, in inches. what trend line models the data shown in the table? what does the slope of the trend line represent?

x	40	43	50	55	60
y	8.3	9	10.4	11.5	12.5

which of the following is an equation of a trend line that models the data?
a. $y = -0.2x - 0.5$
b. $y = 0.2x$
c. $y = -0.2x + 0.5$
d. $y = -0.2x$
e. $y = 0.2x - 0.5$
f. $y = 0.5$
g. $y = 0.2x + 0.5$
h. $y = -0.5$

the slope represents the \\(\boldsymbol{\downarrow}\\) in \\(\boldsymbol{\downarrow}\\) of the maximum recommended viewing distance per \\(\boldsymbol{\downarrow}\\) in screen size

Explanation:

Step1: Analyze the trend (positive/negative)

As \( x \) (screen size) increases, \( y \) (viewing distance) increases, so the slope should be positive. Eliminate options with negative slope (A, C, D, H). Also, \( y \) isn't constant (eliminate F, H). Now check remaining: B (\( y = 0.2x \)), E (\( y = 0.2x - 0.5 \)), G (\( y = 0.2x + 0.5 \)).

Step2: Test with \( x = 40 \)

For \( x = 40 \), \( y = 8.3 \).

• B: \( 0.2(40) = 8 \) (diff: \( 8.3 - 8 = 0.3 \))
• E: \( 0.2(40) - 0.5 = 8 - 0.5 = 7.5 \) (diff: \( 8.3 - 7.5 = 0.8 \))
• G: \( 0.2(40) + 0.5 = 8 + 0.5 = 8.5 \) (diff: \( 8.5 - 8.3 = 0.2 \), closest).

Check \( x = 43 \), \( y = 9 \):

• G: \( 0.2(43) + 0.5 = 8.6 + 0.5 = 9.1 \) (close to 9).

Step3: Interpret the slope

The slope \( 0.2 \) (positive) represents the increase in \( y \) (viewing distance, units: feet) per inch increase in \( x \) (screen size).

Answer:

The equation of the trend line is G. \( y = 0.2x + 0.5 \).
The slope represents the increase in feet of the maximum recommended viewing distance per inch in screen size.