stats help!! pls!!

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

Hi Katie,

For this question we need to write a simple linear equation to express the price P in the form :

P = mn + b

In our linear equation:

m = represents the slope

n = represents the number of shirts ( this is our x value)

b = y intercept

P = price of shirt ( this is our y value)

(*Remember n = x our independent variable and P = y which is our dependent variable*)

A line is always defined by two points and since we have two points on the line ,( (3000, 29) and (8000,9) ), we can find the equation of the line.

Lets find m .

m = the (difference in the y values) / (difference in x values) OR rise / run

m = (9 - 29) / (8000 -3000) = -1/250

Lets find b now .

We know that y = mx + b so lets plug in a value for y and x and see what b is .

y = mx + b => y - mx = b . When x = 3000 and y = 29 what is b?

b = 29 - (-1/250) × (3000) = 41

So now we have m = -1/250 and b = 41 so we can write the equation of our line which is y = mx+ b or

P = (-1/250)x + 41

We can check if this is correct by plugging in some of the points we already have !

When b=8000 P = (-1/250)(8000) + 41= 9 which is the value we were given so we are sure that our linear equation is P = (-1/250)x + 41

Answer 2

note: n = independent variable; p = dependent variable;

p = mn + b; m = (p2 - p1)/(n2 - n1) = ($9 - $29)/(8000 - 3000) = -$20/5000 = -0.004

for n = 8000, p = 9 ---> 0 = -0.004(8000) + b = -32 + b --- > b = 9 + 32 = 41 ---> p = -0.004n + 41