# SAT Math Multiple Choice Question 606: Answer and Explanation

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**Question: 606**

**6.** The cost in dollars, *C*, to manufacture *n* necklaces is given by the equation *C*(*n*) = *an* + *b*, where *a* and *b* are positive constants. In this equation, what does *a* represent?

- A. the fixed costs, in dollars, independent of any necklaces being manufactured
- B. the total cost, in dollars, to produce
*n*necklaces, not including fixed costs - C. the total cost, in dollars, to produce one necklace, including fixed costs
- D. the cost, in dollars, to produce one necklace, not including any fixed costs

**Correct Answer:** D

**Explanation:**

**D**

**Algebra (linear equations) MEDIUM**

*C*(*n*) = *an* + *b*

Since this expression is linear in *n* (the input variable, which represents the number of necklaces produced), the constant *a* represents the slope of this line, which in turn represents the "unit rate of increase," in other words, the increase in total cost for each individual necklace produced.

The constant *b* represents the "*y*-intercept" of this line, which in this case means the costs when *n* = 0 (that is, the fixed costs before any necklaces are produced).