Name: ____________________________________________________ Date: ______________Winter Break ReviewThere is NOT enough room on this sheet of paper to show all of your work. Your work should becompleted neatly on a separate sheet of paper, with ALL work shown and answers clearly indicated.Find the rate of change for each line graphed below. Then write the equation of each line.4yy1. 2. 3.44y222xxx−4 −2 2 4−2−4 −2 2 4−2−4 −2 2 4−2−4−4−4y4. 5. 6.44y4y222xxx−4 −2 2 4−4 −2 2 4−4 −2 2 4−2−2−2−4−4−4Find the rate of change for the line that connects each pair of points. Then write the equation of each line.7. ( 20,8 ) and ( 16,16 ) 8. ( 2, − 5)and ( 7,10 ) 9. ( − 3,4)and ( −7, − 2)10. ( −4, − 5)and ( 3,3 ) 11. ( 3, − 8)and ( − 2,5)12. ( 2,5 ) and ( −3, − 12)13. The natural sweeteners used in foods include sugar, corn sweeteners, syrup, and honey. In 1989, eachperson in the United States consumed an average of 133 pounds of natural sweeteners. The amount ofnatural sweeteners consumed has increased by an average of 2.6 pounds per year. Write a linearequation to find the average consumption of natural sweeteners in any year after 1989.14. In the middle of the 1998 baseball season, Mark McGwire seemed to be on track to break the record forthe most runs batted in. After 40 games, McGwire had 45 runs batted in. After 86 games, he had 87runs batted in. Write a linear equation to estimate the number of runs batted in for any given number ofgames that season.15. The cost for 7 dance lessons is $82. The cost for 11 dance lessons is $122. Write a linear equation tofind the total cost C for l lessons and use the equation to find the cost of 4 lessons.
16. A construction company charges $15 per hour for debris removal, plus a one-time fee for the use of atrash dumpster. The total fee for 9 hours of service is $195. What is the fee for the use of a trashdumpster? Write an equation to find the total fee y for any number of hours x.17. Green Bank charges a monthly fee of $3 for a checking account and $0.10 per check. Savings-R-Usbank charges a $4.50 monthly fee and $0.05 per check.a) Write an equation that represents the monthly costs, MG, for using Green Bank if you use c checks.b) Write an equation that represents the monthly costs, MS, for using Savings-R-Us if you use cchecks.c) How many checks need to be used for the monthly costs to be the same for both banks?d) Write the algebraic equation that shows how many checks need to be used for the monthly costs tobe the same at both banks.e) If you want to be charged less than $5 each month, how many checks can you use at each bank?18. Easy Rider taxi service charges a pick-up fee of $2 and $1.25 for each mile. Luxury Limo taxi servicecharges a pick-up fee of $3.25 and $1 per mile. How many miles need to be driven for both services tocost the same amount?a) Write an equation that represents the cost, CE, for using getting a ride from Easy Rider taxi serviceif you use travel m miles.b) Write an equation that represents the cost, CL, for using getting a ride from Luxury Limo taxiservice if you use travel m miles.c) How many miles must you travel for the cost to be the same for both taxi services?d) Write the algebraic equation that shows how many miles you must travel for the cost to be the samefor both taxi services?e) If you have to travel 7 miles, which taxi service should you use?19. The math department spends $1200 on calculators and then sells the calculators for $80 each.a) Write an equation that represents the amount of money, DM, that is in the math department budgetafter selling c calculators.b) How many calculators must the department sell to break even?c) Write the algebraic equation that shows how many calculators must be sold for the math departmentto break even.For each set of information below, write the equation of the line and then graph the line on a separate sheet ofgraph paper. Clearly label the graph with its appropriate problem number.20. Slope = − 321.1Rate of change = −2y-intercept = 4 y-intercept = − 2Equation: ____________________Equation: ____________________For each equation provided identify the rate of change and y-intercept. Then graph the line on a separate sheetof graph paper. Clearly label the graph with its appropriate problem number.122. y = 2x− 323. y = x − 23Rate of change: _________y-intercept: _______Rate of change: _________y-intercept: _______