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Intermediate Algebra Name _____________________________
Finding Equations of Lines in Applications
- The graph below shows that the projected value, v , of a Guarneri del Gesù violin is a linear function of the age, a , in years, of the violin, for (^261) a 290.
a. Determine the function, v ( a ) represented by this line.
b. Using the function from part a), determine the projected value of a 265-year-old Guarneri del Gesù violin.
c. Using the function from part a), determine the age of a Guarneri del Gesù violin with a projected value of $15million.
d. What is the domain and range of this function?
- The number of calories burned in 1 hour of bicycle riding is a linear function of the speed of the bicycle. A person riding at 12 mph will burn about 564 calories in 1 hour and while riding at 18 mph will burn about 846calories in 1 hour. This information is shown below.
a. Determine a linear function that can be used to estimate the number of calories, C , burned in 1 hour when a bicycle is ridden at r mph, for 6 r 24.
b. Use the function determined in part a) to estimate the number of calories burned in 1 hour when a bicycle is ridden at 20 mph.
c. Use the function determined in part a) to estimate the speed at which a bicycle should be ridden to burn 800 calories in 1 hour.
d. What is the domain and range of this function?
- The gas mileage, m , of a specific car is a linear function of the speed, s , at which the car is driven, for 30 s 60. If the car is driven at a rate of 30 mph, the car’s gas mileage is 35 miles per gallon. If the car is driven at 60 mph, the car’s gas mileage is 20 miles per gallon.
a. Use this data to write the gas mileage, m , as a function of speed, s.
b. Using the function from part a), determine the gas mileage if the car is driven at a speed of 48 mph.
c. Using the function from part a), determine the speed at which the car must be driven to get gas mileage of 40 miles per gallon.
- The manufacturer of baby strollers determines that the supply, s, is a linear function of the selling price, p, for $ 200 p $ 300. If a stroller sells for $210.00, then 20 strollers will be supplied per month. If a stroller sells for $230.00, then 30 strollers will be supplied per month.
a. Use this data to write an equation for the supply, s , as a function of price, p.
b. Using the function from part a), determine the supply when the price of a stroller is $220.00.
c. Using the function from part a), determine the selling price if the supply is 35 strollers.
