Question

A donut shop wanted to determine the best price to sell its donuts. The manager of the shop gathered data from several donut shops in the city for the total cost, y, for different amounts of donuts, x. He created the following scatter plot with a line of fit.

scatter plot titled donut pricing with the x axis labeled number of donuts and the y axis labeled total cost in dollars, with points at 1 comma 1, 2 comma 2 and a half, 5 comma 5, 6 comma 5 and a half, 3 comma 2, 7 comma 7, 4 comma 4, 8 comma 5 and a half, 12 comma 10, 10 comma 9, 9 comma 9, and 8 comma 7, with a line passing through the coordinates 3 comma 3 and 8 comma 7

Find the slope of the line of fit and explain its meaning for the real-world situation.

The slope is 3 over 5, which means when 0 donuts are sold, it is predicted that the shop will earn $0.60.

The slope is 4 over 5, which means when 0 donuts are sold, it is predicted that the shop will earn $0.80.

The slope is 3 over 5, which means for each additional donut sold, the shop is predicted to earn $0.60.

The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80.

Answer 1

(d) The slope is 4/5, which means the shop earns $0.80 for each additional donut sold

Explanation:

You want the slope and its meaning of the line of best fit for data ...

• x = {1,2,5,6,3,7,4,8,12,10,9,8}
• y = {1,2.5,5,5.5,2,7,4,5.5,10,9,9,7}

Best fit line

A calculator tells us the best-fit line has a slope of about 0.84, approximately 4/5. This is the ratio of incremental revenue to incremental donuts sold, so it represents the marginal revenue of selling another donut.

The slope is 4/5, which means for each additional donut sold, the shop is predicted to earn $0.80 — choice D.

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