Question

A company makes t-shirts and their research shows that that price and demand are related linearly: p = mx + b. They know that in order to sell 10 shirts they need to set the price at $26, and in order to sell 20 shirts they need to set the price at $6. Find the linear equation relating price to demand. p= c. Preview

Answer 1

The linear equation relating price to demand for the t-shirts, derived from the given points (10, $26) and (20, $6), is p = -2x + $46.

Step-by-step explanation:

To find the linear equation relating price to demand for the t-shirts, we can use the two given points: (10, $26) and (20, $6). Since the relationship is linear, we can use the slope formula to find the slope (m) of the equation p = mx + b, where p is the price and x is the quantity of shirts sold.

The slope (m) is calculated by dividing the difference in price by the difference in quantity:

m = (Price2 - Price1) / (Quantity2 - Quantity1)

m = ($6 - $26) / (20 - 10)

m = -$20 / 10

m = -2

Now, to find (b), the y-intercept, we can substitute the slope and one of the points into the equation:

$26 = (-2)(10) + b

$26 = -$20 + b

b = $26 + $20

b = $46

Therefore, the linear equation relating price to demand is: p = -2x + $46.