CUNY Bernard M Baruch College Using the Slope to Find the Linear Equation Questions

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Business Finance

CUNY Bernard M Baruch College


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1. A clothing business finds there is a linear relationship between the number of hats, X, it can sell and the price, P, it can charge per hat. Historical data shows that 1,500 hats can be sold at a price of $40, while 2,000 hats can be sold at a price of $30. Find a linear equation in the form P(X) = bx + a that gives the price P they can charge for X hats a. If they gave away the hats for free, how many hats will people take away? b. How much must they reduce the price of the hats in order to sell an additional hat? c. How many hats can be sold at a price of $25 per hat? d. Use MS-Excel to plot a graph of the Demand Curve for hats. 2. A car rental company offers two plans for renting a car. Plan A: $30 per day and $0.18 per mile. Plan B: $50 per day with free unlimited mileage How many miles would you need to drive for plan B to save you money? 3. For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown in Table 1. Assume that the house values are changing linearly. a b. Table 1 (Median Home Values) Year Mississippi Hawaii 1950 $25,200 $74,400 2000 $71,400 $272,700 In which state have home values increased at a higher rate? If these trends were to continue, what would be the median home value in Mississippi in 2010? 4. A phone company charges for service according to the formula: C(n) = 21 +0.08n, where n is the number of minutes talked, and C(n) is the monthly charge, in dollars. a. What is the fixed charge, even if you do not talk on your phone? b. How much are you charged for each minute of talk time (Rate of Change total charges)? c. What is the total charge, if you talked for 300 minutes on the phone? d. Use the MS-Excel graphing tool to Graph the Function C(n) = 21 +.08n for values of n from 50 to 500, in increments of 25.
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Explanation & Answer

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Question 1
Number of hats, X
Price, P
Historical data (X, P)
Point 1 - (1500, $40)
Point 2 - (2000, $30)
Linear equation
Find the slope

Δy 𝑦2 − 𝑦1
Δ𝑥 𝑥2 − 𝑥2

30 − 40
2000 − 1500


= −0.02
Using the slope to find the linear equation

Δy 𝑦2 − 𝑦1
Δ𝑥 𝑥2 − 𝑥2

−0.02 =

𝑦 − 40
𝑥 − 1500

−0.02(𝑥 − 1500) = 𝑦 − 40
−0.02𝑥 + 30 = 𝑦 − 40
𝑦 − 40 = −0.02𝑥 + 30
𝑦 = −0.02𝑥 + 30 + 40
𝑦 = −0.02𝑥 + 70
𝑷(𝑿) = −𝟎. 𝟎𝟐𝑿 + 𝟕𝟎
Number of hats people will take away if they gave hats away for free

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