Question

a researcher modeled the relationship between weekly practice time (x) and music scores (y) for 150 students using the line of best fit y = 4x + 60. decide whether each statement relates to the slope, y - intercept, or neither. answer choices: see all 9 choices drag the answer choices to the correct category over here! most 8 - hour students scored 85 - 95 points. one student scored 85 after 6 hours - above the models prediction. a student practicing 10 hours is predicted to score 100. the model predicts a score of 60 at 0 hours. a student with no practice is expected to score 60.

Explanation:

Step1: Recall the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

Step2: Analyze each statement

• "A student with no practice is expected to score 60": When \(x = 0\) (no practice), \(y=4\times0 + 60=60\). This relates to the \(y\) - intercept (\(b = 60\)).
• "The model predicts a score of 60 at 0 hours": When \(x = 0\), \(y = 60\). This also relates to the \(y\) - intercept.
• "A student practicing 10 hours is predicted to score 100": Substitute \(x = 10\) into \(y=4x + 60\), \(y=4\times10+60=40 + 60=100\). This is a prediction (using the equation of the line, which is based on slope and \(y\) - intercept, but the key here is it's a prediction).
• "One student scored 85 after 6 hours - above the model's prediction": Substitute \(x = 6\) into \(y = 4x+60\), \(y=4\times6 + 60=24+60 = 84\). The student scored 85 (85>84). This is a comparison to the prediction (using the equation, but the main idea is it's a prediction - related statement).
• "Most 8 - hour students scored 85 - 95 points": Substitute \(x = 8\) into \(y=4x + 60\), \(y=4\times8+60=32 + 60=92\). But the statement is about the range of scores for students with a certain practice time. It is a prediction - related statement (using the model's equation for prediction).

Answer:

• "A student with no practice is expected to score 60": \(y\) - intercept
• "The model predicts a score of 60 at 0 hours": \(y\) - intercept
• "A student practicing 10 hours is predicted to score 100": Prediction
• "One student scored 85 after 6 hours - above the model's prediction": Prediction
• "Most 8 - hour students scored 85 - 95 points": Prediction