1. How would you characterize the relationship between the hours spent on homework and the test scores? Explain.
The relationship between hours spent on homework and the test scores seems to follow a general outline of test scores increasing as more homework is done. You can see that with only [tex]1[/tex] hour of study, students seemed to score at most 50% on their tests, while [tex]6[/tex] hours of study resulted in much higher scores, such as 90%. These numbers are indicative of an upward trend of hours spent doing homework and test scores.
2. Paul uses the function [tex]y=5x+45[/tex] to model the situation. What score does the model predict for [tex]3[/tex] hours of homework?
If we treat [tex]x[/tex] as hours of homework and [tex]y[/tex] as our final test score, then our the predicted score for 3 hours of homework is found as follows:
[tex]y=5x+45\\y=5(3)+45\\y=15+45\\y=60[/tex]
The predicted score for this student is a 60% average on tests.
3. What does the number [tex]45[/tex] in Part (b) mean in the context of the situation?
If we follow the guideline for linear equations in slope-intercept form:
[tex]y=mx+b[/tex]
where [tex]b[/tex] represents where the function hits the [tex]y[/tex]-axis, and apply this to the equation in question 2:
[tex]y=5x+45[/tex]
that would represent the minimum achievable test score for the students in the math class. If [tex]b=45[/tex] then the lowest predicted score in the class is 45%.
