jacob distributed a survey to his fellow students asking them how many hours they spent on the internet in…

jacob distributed a survey to his fellow students asking them how many hours they spent on the internet in the past day. he also asked them to rate their mood on a scale from 0 to 10, with 10 being the happiest. a line was fit to the data to model the relationship. which of these linear equations best describes the given model? choose 1 answer: (a) $hat{y}=x + 7.5$ (b) $hat{y}=-x + 7.5$ (c) $hat{y}=-\frac{1}{2}x + 7.5$

jacob distributed a survey to his fellow students asking them how many hours they spent on the internet in the past day. he also asked them to rate their mood on a scale from 0 to 10, with 10 being the happiest. a line was fit to the data to model the relationship. which of these linear equations best describes the given model? choose 1 answer: (a) $hat{y}=x + 7.5$ (b) $hat{y}=-x + 7.5$ (c) $hat{y}=-\frac{1}{2}x + 7.5$

Answer

Explanation:

Step1: Identify slope - direction

The line is decreasing, so the slope (m) of the line is negative. Option A has a positive slope ((m = 1)), so we can eliminate option A.

Step2: Estimate slope value

Pick two points on the line, say ((0.5,7)) and ((4.5,3)). The slope (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 7}{4.5-0.5}=\frac{- 4}{4}=-1).

Step3: Identify y - intercept

The line intersects the y - axis around (y = 7.5). The equation of a line in slope - intercept form is (\hat{y}=mx + b), where (m) is the slope and (b) is the y - intercept. Since (m=-1) and (b = 7.5), the equation is (\hat{y}=-x + 7.5).

Answer:

B. (\hat{y}=-x + 7.5)