Section 2.4 Applications of Linear Equations and Modeling 177 e. If the company offers a weekly rate of $799, is this a better deal than paying by the day for 7 days? f. Find the total cost of driving the car for 4 days if the sales tax is 6%. g. Is it reasonable to use negative values of x in the equation from part (a)? Why or why not? 8. Alex is a sales representative and earns a base salary of $1000 per month plus a 4% commission on his sales for the month. a. Write a linear equation that expresses Alex’s monthly salary y in terms of his sales x. b. Graph the equation. c. What is the y-intercept and what does it represent in the context of this problem? d. What is the slope of the line and what does it represent in the context of this problem? e. How much will Alex make if his sales for a given month are $30,000? Salary ($) Monthly Salary Versus Sales 2500 2000 1500 1000 9. Ava recently purchased a home in Crescent Beach, Florida. Her property taxes for the first year are $2742. Ava estimates that her taxes will increase at a rate of $52 per year. a. Write an equation to compute Ava’s yearly property taxes. Let y be the amount she pays in taxes, and let x be the time in years. b. Graph the line. 4000 3500 2500 2000 1500 1000 c. What is the slope of this line? What does the slope of the line represent in the context of this problem? d. What is the y-intercept? What does the y-intercept represent in the context of this problem? e. What will Ava’s yearly property tax be in 10 years? In 15 years? 10. Millage rate is the amount per $1000 that is often used to calculate property tax. For example, a home with a $80,000 taxable value in a municipality with a 19 mil tax rate would require (0.019)($80,000) $1520 in property taxes. a. In one county, homeowners pay a flat tax of $156 plus a rate of 19 mil on the taxable value of a home. Write a linear equation that represents the total property tax y (in $) for a home with a taxable value of x dollars. b. Determine the amount of property tax on a home with a taxable value of $90,000. c. If the property tax on a home is $2436, determine the taxable value of the home. Sales ($) 3000 500 10,000 20,000 30,000 40,000 50,000 y x Taxes ($) Time (Years) 3000 500 2 4 6 8 10 12 14 16 18 20 y x Yearly Taxes Versus Year
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