Question

Benito embroiders and sells T-shirts. The graph shows his profit as a function of the number of shirts sold. After selling a certain number of shirts, Benito uses some earnings to buy more materials and then increases the price of the shirts. Which of the following is true? A coordinate plane with 12 distinct points plotted which are not connected. The points are 0 comma negative 20, 1 comma negative 10, 2 comma 0, 3 comma 10, 4 comma 20, 5 comma 30, 6 comma 40, 7 comma 50, 8 comma 25, 9 comma 40, 10 comma 55, and 11 comma 70. Group of answer choices The x-intercept represents the shirts he has to sell before making a profit. Benito increases the price after selling 50 shirts. The y-intercept represents the cost of one T-shirt. The domain of the function is x .

Answer 1

The correct option is;

The x-intercept represents the shirts he has to sell before making a profit

Explanation:

The given data are;

(0, -20), (1, -10), (2, 0), (3, 10), (4, 20), (5, 30), (6, 40), (7, 50), (8, 25), (9, 40), (10, 55), (11, 70)

The data show a linear relationship because successive data point increases by the same amount of 10 for x between 0 and 7 and 15 for x between 8 and 11;

Therefore;

Slope, m of the first linear portion using points (2, 0), and, (4, 20) gives;

m = (20 - 0)/(4 - 2) = 10

The equation of the line is therefore;

y - 20 = 10·(x - 4)

y = 10·x - 40 + 20

y = 10·x - 20

The y-intercept (x = 0) is y = -20

The x-intercept (y = 0) is found as follows;

0 = 10·x - 20

20 = 10·x

10·x = 20

x = 20/10 = 2

Therefore, when x = 2 we have;

Profit = y = 10·x - 20 = 10×2 - 20 = 0

Which can be expressed as, he has to sell more than 2 shirts to make profit

Therefore, the correct option is that the x-intercept represents the shirts he has to sell before making a profit.