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.

Question

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 3, 6 comma 5 and a half, 3 comma 2, 7 comma 5, 4 comma 4, 8 comma 4 and a half, 12 comma 7, 10 comma 7, 9 comma 7, and 8 comma 5 and a half, with a line passing through the coordinates 2 comma 2 and 7 comma 5

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

To determine the slope of the line of fit in the scatter plot provided, we use the two points through which the line passes: (2, 2) and (7, 5).

The slope \( m \) is calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the coordinates of the two points into the formula:

\[ m = \frac{5 - 2}{7 - 2} = \frac{3}{5} \]

Therefore, the slope of the line of fit is \( \frac{3}{5} \).

Interpretation in Context:

The slope of \( \frac{3}{5} \) means that for each additional donut sold, the total cost (or revenue) increases by $0.60. This indicates the price per donut, reflecting the relationship between the number of donuts sold and the total revenue. Thus, as the shop sells more donuts, the increase in total earnings can be anticipated to be $0.60 for each additional donut.