Allison's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=58+8.2 x, where y represents the expected quiz score and x represents hours spent on homework that week. What could the number 8.2 represent in the equation? The change in expected quiz score for every additional one hour students spend on their homework. How many hours a student spends studying all year. A student's expected quiz score if they spent 1 hour on their homework. A student's expected quiz score if they spent 66.2 hours on their homework.

Question

Allison's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation  y=58+8.2 x, where  y represents the expected quiz score and  x represents hours spent on homework that week. What could the number 8.2 represent in the equation? The change in expected quiz score for every additional one hour students spend on their homework. How many hours a student spends studying all year. A student's expected quiz score if they spent 1 hour on their homework. A student's expected quiz score if they spent 66.2 hours on their homework.

Bytelearn · Accepted Answer

Understand Equation: Analyze the equation y=58+8.2x to understand what each term represents. In the equation y=58+8.2x, y is the dependent variable representing the expected quiz score, and x is the independent variable representing the hours spent on homework. The number 58 is the y-intercept, which is the expected quiz score when no time is spent on homework (x=0). The number 8.2 is the coefficient of x, which indicates the change in the expected quiz score for each additional hour spent on homework.Interpret Coefficient: Determine what the coefficient 8.2 represents in the context of the problem. Since 8.2 is the coefficient of the independent variable x (hours spent on homework), it represents the rate of change of the expected quiz score with respect to the hours spent on homework. This means that for every additional hour spent on homework, the expected quiz score increases by 8.2 points.Verify Interpretation: Verify that the interpretation of 8.2 aligns with the options provided in the problem. The problem suggests that 8.2 could represent: - The change in expected quiz score for every additional one hour students spend on their homework. - How many hours a student spends studying all year. - A student's expected quiz score if they spent 1 hour on their homework. - A student's expected quiz score if they spent 66.2 hours on their homework.  From our analysis in Step 2, we can confirm that 8.2 represents the change in expected quiz score for every additional one hour students spend on their homework. The other options do not align with the role of the coefficient in the equation.

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