Question

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 10000 shirts can be sold at a price of $58, while 21000 shirts can be sold at a price of $14. 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.

Explanation:

Step1: Calculate the slope $m$

The slope formula for a line $y = mx + b$ (in our case $p=mn + b$) given two points $(n_1,p_1)$ and $(n_2,p_2)$ is $m=\frac{p_2 - p_1}{n_2 - n_1}$. Here, $(n_1,p_1)=(10000,58)$ and $(n_2,p_2)=(21000,14)$. So, $m=\frac{14 - 58}{21000 - 10000}=\frac{- 44}{11000}=- 0.004$.

Step2: Find the y - intercept $b$

We use the point - slope form $p - p_1=m(n - n_1)$ and then rewrite it in the form $p=mn + b$. Using the point $(n_1,p_1)=(10000,58)$ and $m=-0.004$, we have $p-58=-0.004(n - 10000)$. Expand the right - hand side: $p-58=-0.004n+40$. Add 58 to both sides to get $p=-0.004n + 98$.

Answer:

$p=-0.004n + 98$