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 19000 shirts can be sold at a price of $ 34 , while 24000 shirts can be sold at a price of $ 14 . Give a linear equation in the form p = m n + b that gives the price p they can charge for n shirts

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iwillanswer iwillanswer · Answer 1 · 2020-02-14T09:34:29+01:00

p = -0.004n + 110 is the linear equation

Solution:

Let "p" be the price per shirt

Let "n" be the number of shirts

We have to write a linear equation in the form:

p = mn + b

Where, m is the slope of line and b is the y intercept

In particular, historical data shows that 19000 shirts can be sold at a price of $ 34

While, 24000 shirts can be sold at a price of $ 14

Therefore, two points are:

(19000, 34) and (24000, 14)

Find the slope m using the points

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here,

[tex](x_1, y_1) = (19000, 34)\\\\(x_2, y_2) = (24000, 14)[/tex]

Therefore, slope is given as:

[tex]m = \frac{14-34}{24000-19000}\\\\m = \frac{-20}{5000}\\\\m = -0.004[/tex]

Here negative slope means, the more shirts, the lower the price

Now that we have the slope and a point, we can find the equation

[tex]p - y_1 = m(n - x_1)\\\\p - 34 = -0.004(n - 19000)\\\\p - 34 = -0.004n + 76\\\\p = -0.004n + 76 + 34\\\\p = -0.004n + 110[/tex]

Thus the linear equation is found