Question

Samuel would like to rent a booth at his local farmer's market to sell his merchandise. It costs $280 to rent a booth at the farmer's market, and for each item that Samuel sells, x, he profits $40. This can be modeled by the function S(x) = 40x − 280. Based on the graph of the linear function that represents the amount of money Samuel profits, S(x), what is the coordinate of the x-intercept and its interpretation?

(−280, 0); Samuel will begin with a positive profit
(7, 0); After selling 7 items, Samuel will have a positive profit.
(40, 0); After selling 40 items, Samuel will have a positive profit.
(280, 0); After selling 280 items, Samuel will have a positive profit.

Answer 1

The correct interpretation of the final answer of 7 is as given below:

(7, 0); After selling 7 items, Samuel will have a positive profit.

How is the intercept determined?

The intercept of the modelled function is derived by equation the function to zero, in other words, the intercept is the point at which the y and x axes meet

S(x) = 40x − 280

40x-280=0

40x=280

x=280/40

x=7

The clear interpretation of 7 is that the company needs to sell to make a profit

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