A submarine is at a depth of 100 feet below sea level. Then it starts to dive at a rate of 50 feet per minute.Question 1A. For this situation, what is the independentvariable (include units)?B. What is the dependent variable (include units)?C. What is the slope of the line that models thissituation?D. What is the y-intercept of the line that modelsthis situation?Question 2Write the equation of the line that models thesituation using the slope and y-intercept found inparts C and D of question 1.
Question
A submarine is at a depth of 100 feet below sea level. Then it starts to dive at a rate of 50 feet per minute.Question 1A. For this situation, what is the independentvariable (include units)?B. What is the dependent variable (include units)?C. What is the slope of the line that models thissituation?D. What is the y-intercept of the line that modelsthis situation?Question 2Write the equation of the line that models thesituation using the slope and y-intercept found inparts C and D of question 1.
Solution
Question 1: A. The independent variable is time (in minutes). This is because the depth of the submarine changes with time. B. The dependent variable is the depth of the submarine below sea level (in feet). This is because the depth depends on the amount of time the submarine has been diving. C. The slope of the line that models this situation is -50. This is because the submarine is diving at a rate of 50 feet per minute. The negative sign indicates that the submarine is going deeper, so the depth is increasing in a negative direction. D. The y-intercept of the line that models this situation is 100. This is because the submarine starts at a depth of 100 feet below sea level.
Question 2: The equation of the line that models the situation using the slope and y-intercept found in parts C and D of question 1 is y = -50x + 100. This equation shows that the depth of the submarine (y) is equal to the rate of descent (-50 feet per minute) times the amount of time the submarine has been diving (x), plus the starting depth (100 feet).
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