Question

The table shows the number of hours Jake studied for his math tests and his

corresponding grade.

Hours Jake

Studied

(x)

Test

Grade

(y)

1 84

2 91

3 98

Another student, Howie, increased his test scores 6 points for each hour he

studied.

Which statement correctly describes the rate of change between hours studied and

corresponding test scores of the two students?

Answer 1

The rate of change between the number of hours studied and the corresponding test scores for Jake and Howie can be determined. Jake's rate of change is 7 and Howie's rate of change is 6.

Step-by-step explanation:

The rate of change between the number of hours studied and the corresponding test scores can be determined by finding the difference in test scores divided by the difference in hours studied. In this case, we can compare the rate of change for Jake and Howie.

For Jake, the rate of change is found by subtracting the grade for each hour from the previous grade and dividing by 1 (since the difference in hours is always 1): Rate of change for Jake = (91-84)/1 = 7

For Howie, the rate of change is given as 6 points for each hour studied. So the rate of change for Howie is 6.

Therefore, the statement that correctly describes the rate of change between hours studied and corresponding test scores of the two students is that Jake's rate of change is 7 and Howie's rate of change is 6.

Answer 2

Jake's rate of change in test scores per study hour is 7 points per hour, whereas Howie's rate of change is 6 points per hour, indicating Jake has a higher rate of improvement than Howie.

Step-by-step explanation:

The rate of change in a relationship between two variables refers to how one variable changes in relation to the other. Looking at Jake's study hours and test grades, we can determine his rate of change by calculating the difference in test scores divided by the difference in hours studied. For Jake, the grades increase by 7 points for each hour studied ((91-84)/(2-1) or (98-91)/(3-2)).

For Howie, it is stated directly that he increases his test scores by 6 points for each hour he studied. Thus, if we compare the rate of change between the two students, we find that Jake's rate of change is 7 points per hour, while Howie's is 6 points per hour. Therefore, Jake's rate of improvement on his math test scores is higher per hour of study compared to Howie's.