Answer: p = [tex]\frac{-n}{500} +68[/tex]
Step-by-step explanation:
Let n represent the number of shirts and p represent the price, the there is a linear relationship between n and p, then the model equation is given as:
p = mn + b, where
m = slope and b is the intercept
From the question, when n = 1000, p = $66
And, when n = 10,000 , p = $48
The formula for finding slope is given as:
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
[tex]y_{1} = 66[/tex]
[tex]y_{2} = 48[/tex]
[tex]x_{1} = 1000[/tex]
[tex]x_{2} = 10000[/tex]
substituting the values,
m = [tex]\frac{48-66}{10000-1000}[/tex]
m = [tex]\frac{-18}{9000}[/tex]
m = [tex]\frac{-2}{1000}[/tex]
m = [tex]\frac{-1}{500}[/tex]
The linear equation thus becomes
p = [tex]\frac{-n}{500}+b[/tex]
To find the value of b, substitute p = 66 and n =1000 into the equation
That is,
66 = [tex]\frac{-1000}{500}+b[/tex]
66 = -2 + b
68 = b
Therefore b = 68
The linear equation is therefore
p = [tex]\frac{-n}{500} +68[/tex]
