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).
a) There is a positive relationship. When Katie's income increases, so too does her purchase of books.
b) The relationship is plotted in the figure above.
c) The slope equals the change in the value of the variable measured on the vertical axis, income, divided by the change in the value of the variable measured along the horizontal axis, the number of books. Between $50,000 and $70,000 of income, the number of books purchased increases from 14 to 16. Hence income increases by $20,000 and the number of books increases by 2, so the slope equals $20,000/2 = 10,000.
d) As with the previous answer, the slope equals the change in income divided by the change in books. Between $90,000 and $110,000 of income, the number of books purchased increases from 18 to 20. Hence income increases by $20,000 and the number of books increases by 2, so the slope equals $20,000/2 = 10,000.
e) The slopes in parts (c) and (d) are equal. But, they must be equal because the relationship between Katie's income and the number of books she purchases is linear. For a linear relationship, the slope is the same regardless of where it is measured.
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