Applications of Linear Equations Name: _________________________________ Date: _________________ Applications of Linear Equations Please complete the following open ended and multiple choice problems. 1) A rental car company charges a base fee of $45.84 plus $0.45 per mile driven. If x represents the number of miles driven, which of the following equations could be used to find y, the total cost of the bill? y = 0.45x B) y = 0.45x + 45.84 C) y = 45.84x + 0.45 D) y = 46.29x What is the slope of the line? ______________________________________________ What is the y-intercept of the line? __________________________________________ 2) The Bedrock water department has a monthly service charge of $10.70 and a volume charge of $1.54 for every 100 cubic feet of water used. Which of the following equations can be used to determine your family’s monthly water bill? (Let x represent 100 cubic feet of water and y represent the monthly cost). A) y = 1.54x + 10.70 B) y = 1.54x – 10.70 C) y = 12.24x D) y = 0.0154x + 10.70 If your family uses NO water this month, what will your bill be? _____________________ Does the answer to the previous question refer to the slope or y-intercept? ____________ 3) Marc works as a salesman at a car dealership. He is paid a base salary of $1,266.48 each month, and he receives a commission of $160.79 for each vehicle he sells. If last month Marc earned $6,411.76, how many cars did he sell last month? A) 40 B) 64 C) 32 D) 80 If Marc sold NO cars last month, what would his pay be for that month? _______________ 4) The cost of a long distance phone call is modeled by the function, C(m) = 0.15m + 1 where C(m) is the Cost in dollars and m is the length of the call in minutes. Determine how long a phone call was if its cost was $9.25. A) 55 minutes B) 61 minutes C) 50 minutes D) 110 minutes How much more money are you charged for each additional minute that you stay on the phone? _______________________________________________________________ Does the answer to the previous question refer to the slope or the y-intercept? _________

5) Parking charges at Superior Parking Garage are $5 5) Parking charges at Superior Parking Garage are $5.00 for the first hour and $1.50 for each additional 30 minutes. If Margo has $12.50, what is the maximum amount of time she will be able to park her car at that garage? A) 2.5 hours B) 6 hours C) 3.5 hours D) 6.5 hours 6) Tara buys two items that cost d dollars each. She gives the cashier $20. Which expression represents the change she should receive? 20 – 2d B) 20 + 2d C) 20 – d D) 2d - 20 7) The amount of Jerry’s pay every week before taxes, J, is given below as a function of the number of overtime hours that he works (number of hours past 40), h. J = 493.60 + 18.51h How much money does Jerry make before starting any overtime? ____________________ How many hours does Jerry have to work before starting any overtime? _______________ How much money does Jerry make per hour of regular time? ________________________ How much money does Jerry make per hour of overtime? __________________________ Assuming that Jerry is only paid for each whole hour that he works, how many total hours would Jerry have to work during a week to make at least $800? A) 16 B) 67 C) 57 D) 56 8) Tim has a savings account. His balance was $600 when he decided to start making weekly deposits (he deposits the same amount each week). The table below shows the value of his account (y) after each weekly deposit (x). How much does Tim deposit each week? _______________________________________ If his account continues to increase at the same rate, what will be the value of his account after he makes his 6th deposit? A) $1,925 B) $2,175 C) $1,950 D) $1,725

9) Examine the graph of the line below 9) Examine the graph of the line below. Select the x-y table that represents a set of 5 points on that line. A) B) C) D) State the equation of the line in slope intercept form. ____________________________ 10) A university completed a study to determine what effect drinking coffee had on hours of sleep. After studying many subjects, they concluded the following relationship between number of cups of coffee and hours of sleep: s = − 2 3 c + 8 where s represents the number of hours of sleep and c represents the number of cups of coffee a person drinks How long would you expect a person who drank NO coffee to sleep? __________________ Does the previous question refer to the slope or y-intercept? _______________________ For each additional cup of coffee a person drinks, how many less hours of sleep would you expect them to get? _____________________________________________________ Graph the function: Identify the x-intercept: _______ What does that mean in the context of this problem? __________________________________________________________________________________________