a clothing business finds there is a linear relationship between the number of shirts, n, it can sell and…

a clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. in particular, historical data shows that 6000 shirts can be sold at a price of $53, while 7000 shirts can be sold at a price of $44. give a linear equation in the form p = mn + b that gives the price p they can charge for n shirts. answer: p = round the value of your slope to three decimal places. be careful to use the proper variable and use the preview button to check your syntax before you submit your answer. question help: video post to forum

a clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. in particular, historical data shows that 6000 shirts can be sold at a price of $53, while 7000 shirts can be sold at a price of $44. give a linear equation in the form p = mn + b that gives the price p they can charge for n shirts. answer: p = round the value of your slope to three decimal places. be careful to use the proper variable and use the preview button to check your syntax before you submit your answer. question help: video post to forum

Answer

Explanation:

Step1: Find two points

We have two points ((n_1,p_1)=(6000,53)) and ((n_2,p_2)=(7000,44)) for the linear - relationship (p = mn + b).

Step2: Calculate the slope (m)

The slope (m=\frac{p_2 - p_1}{n_2 - n_1}=\frac{44 - 53}{7000 - 6000}=\frac{-9}{1000}=- 0.009).

Step3: Find the y - intercept (b)

Substitute (m=-0.009), (n = 6000), and (p = 53) into (p=mn + b). (53=-0.009\times6000 + b). (53=-54 + b). (b=53 + 54=107).

Step4: Write the linear equation

The linear equation is (p=-0.009n + 107).

Answer:

(p=-0.009n + 107)