Question

(a) How would you characterize the relationship between the hours spent on homework and the test scores (Positive or Negative, Linear or Non-Linear)? Explain.

(b) Paul used the function y= 8x + 40 to model the situation. What score does the model predict for 4 hours of homework?


(c) What does the number 40 in Part (b) mean in the context of the situation?


Please don’t answer if you are guessing. Answer if you really know the answer. And if you don’t understand the three questions, answer the ones you do know.

Answer 1

a) Positive linear

b) 72

c) Marks scored when no time is spend on homework.

Explanation:

a) relationship between the hours spent on homework and the test scores

As the time spent on homework increases the test score increases.

Similarly if less time is spent on homework, there would be a decrease in test score.

The two variables are directly related.

Thus, there relationship can be expressed as a positive linear relationship.

b) The model function

`y= 8x + 40`

where y is the test score and x is the time spent on homework in hours.

Score predicted by model when x = 4

`y(4)= 8(4) + 40 = 32 +40 = 72`

Thus, model predict that the score on test will be 72 when 4 hours are spent on homework.

c) Interpretation of 40

When x = 0

`y(0)= 8(0) + 40 = 40`

Interpretation:

Thus, when Paul spends no time on homework that is zero hours are spend on homework, then, Paul will score 40 on test.