calculus maths work

Question

A clothing business finds there is a linear relationship between the number of shirts,,it can sell and the price,, it can charge per shirt. In particular, historical data shows that  shirts can be sold at a price of , while  shirts can be sold at a price of . Give a linear equation in the form  that gives the price  they can charge for  shirts.

Answer 1

We are given two data points in the form (n, p) i.e., ("number of shirts", "price of shirt") which are:

(6000, 44) and (17000, 22)

A linear relationship means the slope is the same everywhere. The slope is the change in the dependent variable (this time that is "p") divided by the change in the independent variable (this time that is "n").

So the slope (which we call "m") is (p₂ - p₁) divided by (n₂ - n₁) or

so m = (22 - 44)/(17000 - 6000) = -22/11000 = -0.002 and the units of that is $/shirt. So the price of the shirts are dropping 0.002 dollars per shirt as the number of shirts goes up.

plugging that value of "m" into the basic equation p = mn + b we get p = -0.002n + b. Now, we need to calculate "b". To do so, pick one of the points and plug it into the equation as the values of "n" and "p". Let's use (6000, 44) to make n = 6000 and p = 44:

p = -0.002n + b

44 = -0.002(6000) + b

44 = -12 + b

b = 56

So plugging that value of "b" into the equation gives us p = -0.002n + 56

Answer 2

p = mn + b;

We have 2 pints: (6000, 44) and (17000, 22).

44 = 6000m + b and 22 = 17000m + b;

22 = - 11000m; m = - 22/11000 = - 0.002; b = 44 - 6000(- 0.002) = 56.

p = - 0.002n + 56

Answer 3

Uses two-;point form from Algebra 1

(6000, 44), (17000, 22)

(p - 44) / (n - 6000) = (22 - 44) / 17000 - 6000)

Can you simplify and convert to slope-intercept form?