Question

Arturo'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 y=56+8.2x, where y represents the expected quiz score and xx represents hours spent on homework that week. What is the meaning of the y=89?

Answer 1

The equation y=56+8.2x represents the linear relationship between time spent on homework and quiz scores. The equation y=89 means that the expected quiz score is 89. By substituting 89 into the equation, the corresponding amount of time spent on homework can be found.

Step-by-step explanation:

The equation y=56+8.2x represents the linear relationship between the amount of time students spend on their homework (x) and their expected quiz scores (y). In this equation, the constant term (56) represents the expected quiz score if the student does not do any homework, and the coefficient of x (8.2) represents the increase in the expected quiz score for each additional hour of homework.

Now, let's look at the equation y=89. In this case, 89 represents the expected quiz score. To find the corresponding amount of time students spend on homework (x), we can substitute 89 into the equation and solve for x. Rearranging the equation, we have 89=56+8.2x. Subtracting 56 from both sides, we get 33=8.2x. Dividing both sides by 8.2, we find that x is approximately 4.02 hours.

Therefore, if a student spends around 4.02 hours on homework, their expected quiz score would be 89.