10) The figure above shows how the relationship between the number of hours per week a high school student spends on the web and the student's SAT score. Is the relationship between hours on the web and the SAT score positive, negative, neither? Explain your answer.
Answer: The figure shows that there is a negative relationship between hours on the web and the student's SAT score. The relationship is negative because the two variables move in opposite directions: If hours on the web increase, the SAT score decreases.
Topic: Negative relationship
Skill: Level 2: Using definitions
Section: Chapter 1 Appendix - Checkpoint 2
Status: Old
AACSB: Analytic skills
11) A graph has a point that is either a maximum or a minimum. To the left of the point, the slope of relationship is positive. To the right of the point, the slope is negative. Is the point a maximum point or a minimum point? Be sure to draw a figure that supports your answer.
Answer:
The point is a maximum point. Examine the figure above. The slope of a curved line at any point equals the slope of a straight line that touches the curved line at only that one point. Thus to the left of the maximum point, take point A. The slope of the straight line that touches the curved line at only point A is positive, so the slope of the relationship is positive. Similarly, take point B to the right of the maximum point. As the straight line shows, the slope of the relationship at point B is negative. Indeed, whenever there is a maximum point, the slope of the relationship to the left of the maximum is positive and the slope to the right is negative.
Topic: Maximum
Skill: Level 1: Definition
Section: Chapter 1 Appendix - Checkpoint 2
Status: Old
AACSB: Analytic skills
12) What does the slope of a straight line equal? How is the slope of a curved line calculated?
Answer: The slope of a straight line is calculated between two points on the line. Between the two points on the line, the slope equals the change in the value of the variable measured on the vertical axis (the y-axis) divided by the change in the value of the variable measured on the horizontal axis (the x-axis). The slope of a curved line is calculated at a point on the line. At that point on the curved line, draw a straight line that touches the curved line at only that point. Then, calculate the slope of the straight line. The slope of the curved line at that point equals the slope of the straight line.
Topic: Slope
Skill: Level 1: Definition
Section: Chapter 1 Appendix - Checkpoint 3
Status: Old
AACSB: Analytic skills
13) In the figure above, what can you deduce about the slope of the curve?
Answer: The slope is positive and increasing in size as we move rightward along the curve.
Topic: Slope
Skill: Level 2: Using definitions
Section: Chapter 1 Appendix - Checkpoint 3
Status: Old
AACSB: Analytic skills
14) The table above shows how the number of books Katie buys each year depends on her income.
a. What kind of relationship exists between Katie's income and the number of books she purchases?
b. Plot the relationship between Katie's income and the number of books she purchases in the above figure. Measure income along the vertical axis and the number of books along the horizontal axis. Be sure to label the axes.
c. What is the slope of the relationship between $50,000 and $70,000 of income?
d. What is the slope of the relationship between $90,000 and $110,000 of income?
e. Comment on the similarity or dissimilarity of your answers to parts (c) and (d).