Question

In particular, historical data shows that 7000 shirts can be sold at a price of $71, while 9000 shirts can be sold at a price of $57. Give a linear equation in the form p=mn+b that gives the price p they can charge for shirts.

Answer 1

The linear equation that gives the price of shirts depending on the number sold is p = -0.007n + 120.

Step-by-step explanation:

The given information states that 7000 shirts can be sold at a price of $71, and 9000 shirts can be sold at a price of $57. We can use this information to find the equation of the line that represents the relationship between the number of shirts sold and the price. Let's call the number of shirts sold x and the price p. Using the two points (7000, 71) and (9000, 57), we can find the slope (m) and y-intercept (b) of the line.

Slope (m) = (change in y) / (change in x)

m = (57 - 71) / (9000 - 7000) = -14 / 2000 = -0.007

Next, we can use one of the points and the slope to find the y-intercept (b). Let's use the point (7000, 71).

p = mx + b

71 = -0.007(7000) + b

71 = -49 + b

b = 120

Therefore, the linear equation in the form p = mn + b that gives the price p they can charge for shirts is: p = -0.007n + 120