Pete took 3 history tests last quarter. For the first test, he studied for 65 minutes and scored 87%. For the second test, he studied for 45 minutes and scored 73%. For the third test, he studied for 80 minutes and scored 98%. Is the relationship between the amount of time Pete studied and the resulting test score a linear relationship? Choices: (A)yes (B)no Now, justify your answer. Choices: (A)The longer Pete studied, the better his test score. (B)Pete's test scores increased by 7 points for every additional 10 minutes of study time. (C)The increase in Pete's test score for every additional minute of study time is not constant. (D)Pete's test score decreased from the first test to the second test and then increased from the second test to the third test.

Question

Pete took 3 history tests last quarter. For the first test, he studied for 65 minutes and scored 87%. For the second test, he studied for 45 minutes and scored 73%. For the third test, he studied for 80 minutes and scored 98%. Is the relationship between the amount of time Pete studied and the resulting test score a linear relationship?   Choices: (A)yes (B)no  Now, justify your answer.   Choices: (A)The longer Pete studied, the better his test score. (B)Pete's test scores increased by 7 points for every additional 10 minutes of study time. (C)The increase in Pete's test score for every additional minute of study time is not constant. (D)Pete's test score decreased from the first test to the second test and then increased from the second test to the third test.

Bytelearn · Accepted Answer

Analyze Data Points:  Step 1: Analyze the given data points for Pete's study time and test scores. We have three pairs of data: (65, 87), (45, 73), and (80, 98). Calculate Rate of Change:  Step 2: To determine if the relationship is linear, calculate the rate of change between each pair of points. First, find the change in score and the change in study time between the first and second tests. Change in score = 73 - 87 = -14. Change in study time = 45 - 65 = -20. Determine Linearity:  Step 3: Calculate the rate of change from the first calculation. Rate of change = Change in score / Change in study time = -14 / -20 = 0.7. Repeat Rate of Change:  Step 4: Repeat the rate of change calculation for the second and third tests. Change in score = 98 - 73 = 25. Change in study time = 80 - 45 = 35. Rate of change = 25 / 35 ≈ 0.714. Compare Rates:  Step 5: Compare the rates of change. If they are equal, the relationship might be linear. The rates of change calculated are approximately 0.7 and 0.714, which are not exactly the same but very close. This suggests a nearly linear relationship, but slight differences indicate it might not be perfectly linear.

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