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We are tasked with finding a linear equation that describes the relationship between the number of shirts sold $n$ and the price per shirt $p$. The equation will be of the form:

\[
p = mn + b
\]

where $m$ is the slope and $b$ is the y-intercept.

### Given Data:
- $n_1 = 3000$, $p_1 = 122$ (3000 shirts sold at $122)
- $n_2 = 19000$, $p_2 = 26$ (19000 shirts sold at $26)

### Step 1: Find the slope $m$
The slope $m$ is calculated using the formula:

\[
m = \frac{p_2 - p_1}{n_2 - n_1}
\]

Substituting the values:

\[
m = \frac{26 - 122}{19000 - 3000} = \frac{-96}{16000}
\]

Now let's compute the slope.The slope $m$ is $-0.006$.

### Step 2: Find the y-intercept $b$

Now that we have the slope, we can use one of the points to find the y-intercept $b$. Using the point $(n_1, p_1) = (3000, 122)$, we substitute into the equation:

\[
p_1 = mn_1 + b
\]

Substituting the known values:

\[
122 = (-0.006)(3000) + b
\]

Now, we solve for $b$.The y-intercept $b$ is 140.

### Final Equation:
The linear equation relating the number of shirts sold $n$ and the price per shirt $p$ is:

\[
p = -0.006n + 140
\]

Would you like further explanation on any part of this? 

Here are some related questions:
1. How does changing the slope affect the price for different quantities of shirts?
2. What does the y-intercept represent in this context?
3. How can you use this equation to predict prices for other quantities of shirts?
4. What would happen if you sold 25,000 shirts? What price could be expected?
5. How would you calculate the number of shirts that could be sold at a price of $50?

**Tip:** When calculating the slope, always pay attention to the units and context to interpret the result correctly!

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. Historical data shows that 3000 shirts can be sold at a price of $122, while 19000 shirts can be sold at a price of $26. Give a linear equation in the form p = mn + b that gives the price p they can charge for n shirts.

Learn how to find a linear equation that models the relationship between the number of shirts sold and the price per shirt. Using data points like 3000 shirts sold for $122 and 19000 shirts for $26, this problem explains how to calculate the slope and y-intercept for the equation p = -0.006n + 140.

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