Questions: Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports 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) ŷ = 5x + 1.5 (B) ŷ = 1.5x + 5 (C) ŷ = -1.5x + 5

Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports 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) ŷ = 5x + 1.5 (B) ŷ = 1.5x + 5 (C) ŷ = -1.5x + 5
Transcript text: Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports 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) $\hat{y}=5 x+1.5$ (B) $\hat{y}=1.5 x+5$ (c) $\hat{y}=-1.5 x+5$
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Slope of the Line

To determine the slope of the line, we need to find the change in the mood rating (y-axis) over the change in hours playing sports (x-axis). From the graph, we can see that as the hours playing sports increase from 0.5 to 1.5 (a change of 1 hour), the mood rating increases from 4 to 5.5 (a change of 1.5).

Slope (m) = Change in y / Change in x = 1.5 / 1 = 1.5

Step 2: Identify the Y-Intercept

The y-intercept is the point where the line crosses the y-axis (when x = 0). From the graph, we can see that the line crosses the y-axis at approximately 5.

Step 3: Form the Equation of the Line

Using the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, we can form the equation:

y = 1.5x + 5

Final Answer

The linear equation that best describes the given model is:

B) \( \hat{y} = 1.5x + 5 \)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Multiple Choice Question An auto worker in Michigan who loses her job because the company relocated the plant to another country is an example of: seasonal unemployment frictional unemployment cyclical unemployment structural unemployment
failedAnswered
Part 3 of 7 0 of 1 Point The number of fish in a commercial pond can be modeled by the following function F(t) = 401 - 401 e^(-0.29 t), where F(t) is the number of fish in month t. (a) Graph the function. (b) Estimate the number of fish in the pond in month 0, 1, 5, 10, and 15. (c) Is there a maximum number of fish this pond can accommodate? If yes, how many?
failedAnswered
Submit Quiz the value of the qurota a?
failedAnswered
Identify each pair of angles as adjacent, vertical, complementary, supplementary, and/or as a linear pair (questions 20 thru 25). (Name in as many ways as possible) angle AFB and angle CFB
failedAnswered
Meningitis Identify the chosen disease. What are the causes? What are the risk factors? Give a brief definition and describe in detail the pathophysiology of the disorder. Explain how the disorder works at a cellular level and interacts with other chemicals or cells in the body. What are the common clinical manifestations of the disease/disorder according to your resources? Explain WHY or WHAT causes the clinical manifestations that you see. Describe the common complications of this disorder/disease according to your resources. Explain the relationship between the disorder and the complication. Explain what causes the complications. What diagnostic tests are used to diagnose the disease/disorder?