By calculating the slope and y-intercept from the given data points, we derived the linear equation p = 4n + 50, which predicts the clothing business can charge $650 for 150 shirts.
Finding the Linear Equation for Shirt Pricing
To find the linear equation that relates the number of shirts sold (n) to the price per shirt (p), we can use the two data points provided: (50, $250) and (100, $450). First, we calculate the slope (m) of the line:
Slope (m) = (Change in price) / (Change in shirts) = ($450 - $250) / (100 - 50) = $200 / 50 = $4 per shirt.
Now, we round the slope to three decimal places, which gives us m=4.000. Next, we use one of the data points to compute the y-intercept (b). Let's use the first point (50, $250).
p = mx + b 250 = 4(50) + b 250 = 200 + b b = $250 - $200 b = $50
The y-intercept b is $50. Therefore, the linear equation describing the relationship is p = 4n + 50.
To forecast the price at which 150 shirts could be sold, we substitute n with 150:
p = 4(150) + 50 p = 600 + 50 p = $650
So, the business can potentially charge $650 for 150 shirts, assuming the linear relationship continues.
The probable question may be:
In the dynamic world of online retail, a clothing business discovers a linear relationship between the number of shirts (n) it can sell and the price (p) it can charge per shirt. Historical data reveals that 50 shirts can be sold at a price of $250, while 100 shirts can be sold at a price of $450.
Now, let's expand the data:
Number of Shirts (n)Price (p)
50 250
100 450
150 ?
Additional Information: The clothing business anticipates selling 150 shirts and is curious about the potential price it could charge. Assuming a linear relationship, derive the linear equation in the form p=mx+b, where m is the slope and b is the y-intercept. Round the value of the slope (m) to three decimal places.