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 )

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).

Step2: Test remaining options (B, E, G)

• For option B (\( y = 0.2x \)): At \( x = 40 \), \( y = 0.2(40) = 8 \). Actual \( y = 8.3 \), close but let's check G.
• For option G (\( y = 0.2x + 0.5 \)): At \( x = 40 \), \( y = 0.2(40)+0.5 = 8 + 0.5 = 8.5 \). Closer to 8.3.
• For option E (\( y = 0.2x - 0.5 \)): At \( x = 40 \), \( y = 0.2(40)-0.5 = 8 - 0.5 = 7.5 \), which is lower than 8.3.
• Check another point: \( x = 60 \), G gives \( y = 0.2(60)+0.5 = 12 + 0.5 = 12.5 \), which matches the table's \( y = 12.5 \).

Answer:

G. \( y = 0.2x + 0.5 \)