Question

Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $11,000 in 1982 and $52,500 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales S(x).

Options:
A) S(x) = 9,500x + 11,000
B) S(x) = 8,700x + 11,000
C) S(x) = 9,500x + 52,500
D) S(x) = 8,700x + 52,500

Answer 1

The correct equation for the yearly sales S(x) based on the given data is S(x) = 8,300x + 11,000, but it is not listed among the provided options. The closest option is B with an incorrect slope.

Step-by-step explanation:

The student is asking for the linear equation that models the sales of an appliance dealer given two data points: sales of $11,000 in 1982 and $52,500 in 1987. We assume that x = 0 represents the year 1982. To find the slope of the line (rate of change of sales per year), we calculate the difference in sales divided by the difference in years. The slope, m, is ($52,500 - $11,000) / (1987 - 1982) = $41,500 / 5 = $8,300 per year. The equation of the line is then S(x) = mx + b, where m is the slope and b is the y-intercept (sales at x = 0, or 1982).

Since the sales were $11,000 in 1982, b = $11,000. The complete linear equation for the yearly sales S(x) is:

S(x) = 8,300x + 11,000

None of the provided options are correct, but the correct equation is closest to option B, though the slope is incorrect in that choice.