Answer:
- Library 2 charges more for each book loaned.
- Library 1 has a cheaper subscription fee.
Step-by-step explanation:
Based on the table, we can write the equation for the cost of borrowing from Library 2 using the two-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
for (x1, y1) = (2, 15.50) and (x2, y2) = (8, 26) this equation becomes ...
y = (26 -15.50)/(8 -2)(x -2) +15.50 . . . . . fill in the values
y = (10.50/6)(x -2) +15.50 . . . . . . . . . . . . simplify a bit
y = 1.75x -3.50 +15.50 . . . . . . simplify more
In the above, we have x = number of books; y = cost. We can use "n" and "C" for those, respectively, as in the equation for Library 1. Then the monthly cost for Library 2 is ...
C = 12 + 1.75n . . . . . . . arranged to the same form as for Library 1
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Now, we can answer the questions.
Library 2 charges more for each book loaned. (1.75 vs 1.50 for Library 1)
Library 1 has a cheaper subscription fee. (10 vs 12 for Library 2)
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The numbers in the cost equations are ...
C = (subscription fee) + (cost per book loaned)·n
