46 CHAPTER 1 Graphs In Problems 115–118, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. 115. 116. 117. 118. Applications and Extensions 119. Geometry Use slopes to show that the triangle whose vertices are ( ) −2, 5 , ( ) 1, 3 , and ( ) −1, 0 is a right triangle. 120. Geometry Use slopes to show that the quadrilateral whose vertices are ( ) − 1, 1, ( ) 4, 1 , ( ) 2, 2 , and ( ) 5, 4 is a parallelogram. 121. Geometry Use slopes to show that the quadrilateral whose vertices are ( ) ( ) ( ) − − 1,0 , 2,3 , 1, 2 ,and ( ) 4, 1 is a rectangle. 122. Geometry Use slopes and the distance formula to show that the quadrilateral whose vertices are ( ) 0, 0 , ( ) 1, 3 , ( ) 4, 2 , and ( ) − 3, 1 is a square. 123. Truck Rentals A truck rental company rents a moving truck for one day by charging $39 plus $0.60 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 110 miles? 230 miles? 124. Cost Equation The fixed costs of operating a business are the costs incurred regardless of the level of production. Fixed costs include rent, fixed salaries, and costs of leasing machinery. The variable costs of operating a business are the costs that change with the level of output.Variable costs include raw materials, hourly wages, and electricity. Suppose that a manufacturer of jeans has fixed daily costs of $1200 and variable costs of $20 for each pair of jeans manufactured. Write a linear equation that relates the daily cost C, in dollars, of manufacturing the jeans to the number x of jeans manufactured. What is the cost of manufacturing 400 pairs of jeans? 740 pairs? 125. Cost of Driving a Car The annual fixed costs of owning a small sedan are $6578, assuming the car is completely paid for. The cost to drive the car is approximately $0.28 per mile. Write a linear equation that relates the cost C and the number x of miles driven annually. Source: Bureau of Transportation Statistics 126. Wages of a Car Salesperson Dontrell receives $525 per week for selling new and used cars. He also receives 5% of the profit on any sales. Write a linear equation that represents Dontrell’s weekly salary S when he has sales that generate a profit of x dollars. 127. Rental Car Rates Anita’s car is in the auto shop for repairs that should take one day. She found a local car rental company that charges a fee of $17 per day plus 13 cents per mile, with a limit of 150 miles per day. Credit: asiandelight/Shutterstock (a) Write a linear equation that relates the charge C, in dollars, to the number x of miles driven, where ≤ ≤ x 0 150. (b) Graph this equation. (c) What is the charge for driving 50 miles? (d) What is the charge for driving 120 miles? (e) Interpret the slope of the line. 128. Cellular Phone Rates T-Mobile offers an Essentials rate plan for one phone line with autopay that costs $60 per month. The Essentials plan includes unlimited talk and text within the United States, with international calls costing $0.25 per minute. (a) Write a linear equation that relates the charge C, in dollars, to the number x of minutes of international calls. (b) Graph this equation. (c) What is the total charge for one month with 20 minutes of international calls? (d) What is the total charge for one month with 60 minutes of international calls? (e) Interpret the slope of the line. Source: T-Mobile, April 2023. 129. Measuring Temperature The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find a linear equation relating °C and °F if 0°C corresponds to 32°F and 100°C corresponds to 212°F. Use the equation to find the Celsius measure of 70°F. 130. Measuring Temperature The Kelvin (K) scale for measuring temperature is obtained by adding 273 to the Celsius temperature. (a) Write a linear equation relating K and °C. (b) Write a linear equation relating K and °F (see Problem 129).
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