Question

Reasoning  A store sells packages of comic books with a poster. A poster and 8 comics cost ​$13.75. A poster and 17 comics cost ​$22.75. Write a linear function rule that models the cost y of a package containing any number x of comic books.
Suppose another store sells a similar​ package, modeled by a linear function rule with initial value ​$7.75. Use pencil and paper. Explain which store has the better deal.
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Part 1
The linear function rule is yequals
  
enter your response here.

Answer 1

Slope m = (22.75 − 13.75)/(17 − 8) = 9/9 = 1.
Intercept b = 13.75 − 1·8 = 5.75.

So the linear rule is y = x + 5.75.

The other store has initial value $7.75 (y = x + 7.75 if the per‑comic price is the same). Because 5.75 < 7.75, the first store is $2 cheaper for any number of comics, so the first store is the better deal.