Question

A clothing business finds there is a linear relationship between the number of shirts, n n ,it can sell and the price, p p , it can charge per shirt. In particular, historical data shows that 16000 16000 shirts can be sold at a price of $ 69 $ 69 , while 35000 35000 shirts can be sold at a price of $ 12 $ 12 . Give a linear equation in the form p

Answer 1

Answer:

P = -0.003X + 117

Explanation:

First lets define what is a linear relationship:

A linear relationship is a trend in the data that can be modeled using a straight line, so the relationships can be positive (if one variable increases, the other increases in equal proportion), negative (if one variable decreases, the other increases in equal proportion) or nonlinear.

The general equation is:

y = mx + b

Where m is the slope (percent of change of a variable when the other changes by 1 unit) and b is the Y intercept (where a line crosses the y-axis of a graph)

The equation for m is:

$m=\frac{y1 - y2}{x1 - x2}$

If we define p (price) as our y and number of shirts (n) as our x then:

$m=\frac{69 - 12}{16,000 - 35,000}= -0.003$

Now we just replace to find the Y intercep (b)

69 = -0.003(16,000) + b

69 = -48 + b

b = 69 + 48

b = 117

It would give the same result if we use p = 12 and x = 35,000

So the linear equation in the form of p would be :

P = -0.003X + 117

This is a negative linear relationship which means that the more shirts sold, the lower the price.