Review Unit 4: Linear Functions You may use a calculator. Unit 4 Goals Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. (8.EE.5) Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the origin and the equation y= mx+b for a line intercepting the vertical axis at b. (8.EE.6) Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions. (8.F.2) Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. (8.F.3) Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationships or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or table of values. (8.F.4) You may use a calculator. Define variables and create equations for each of the following linear situations. 1. You spend $10 on each gift for a family member. 2. There are 2 teachers for every 35 students on the field trip. 3. You have $4000 in your bank account, and you pay $450 for every 12 months of cell phone service. 4. You owe your parents $75 for the dish you broke. You earn $15 every 2 weeks in allowance. Use the given equation to solve the linear questions. 5. If you collected 1400 Mario coins (), how many stars () would you receive if you followed the equation =? 6. How many cars can you service () if you have 120 tires () and you followed the equation =4? 166
7. If it costs $36 to enter a carnival plus $2 for each ticket to play games (), you would spend a total amount of money () based on the equation =236. How many games can you play if you have $50 to spend? 8. If a recipe for lasagna calls for cup cheese for every layer () plus 1 cup of cheese on top, you would use a total amount of cheese () based on the equation = 1. How many cups of cheese would you need if you wanted to make 4 layers? Create a graph for each of the following linear situations or equations. 9. Grandma makes cinnamon butter by mixing 6 tablespoons of cinnamon (c) for every 2 pounds of butter (b). 10. A snail travels at a speed of 1 foot (d) for every 2 minutes (m). 11. You drink 2 cups of water when you wake up and 3 cups of water (w) every 2 hours (h) throughout the day. 12. A runner gets a 4 meter head start and then travels at a speed of 3 meter m every 8 seconds s. 167
Use the given graph to solve the linear questions. 13. How much would it cost for 14 gallons of gas? 14. How many scoops of ice cream would you need with 4 scoops of cookie dough? Cost in Dollars Gallons of Gas Scoops of Ice Cream 15. How many hours would you have to work to earn $50? 16. How many calories would you burn if you walked for 2 hours? Give the equation for the following linear graph or table. 17. The cost of ice cream () per pound (). 18. Temperature () of water on a stove over time in minutes (). Cost of Ice Cream Money Made Scoops of Cookie Dough Hours Worked Hours Walked Temperature Calories Burned Weight in pound Time in Minutes 168
19. The amount of money for doing chores each week (). 3 5 7 9 11 $59 $75 $91 $107 $123 20. The total cost to buy candy bars. 2 4 6 8 10 $4 $6 $8 $10 $12 Fill out the table for each of the following linear situations, equations or graphs. 21. Monty sells used video games where total cost for customers is $50 for each set of 3 games plus there is a $10 warranty fee. 3 9 15 $110 $210 22. The amount of trumpets compared to flutes is based on the following equation:. 9 15 21 4 6 23. The graph shows the average number of eggs produced by a herd chickens in a day. Eggs produced 30 60 90 6 10 Days Use the given table to solve the linear questions. 24. How many teaspoons of sugar would you need in 16 cups of coffee? 1 2 3 4 5 2 4 6 8 10 25. How many nights could you stay in a hotel if you can spend $2000? 1 3 5 7 9 $500 $1100 $1700 $2300 $2900 169
Answer the following questions comparing linear function equations and descriptions. Carla s Cookies is looking for a new machine to make their cookies. Here is the information about the amount of cookies made () in terms of time () in minutes and power consumption () in watts of electricity in terms of time () in minutes for the machines. Machine A: Cookies made is modeled by the equation 23 Power consumption is modeled by the equation 3.54 Machine B: Cookies made is modeled in the following table 10 20 30 40 50 200 400 600 800 1000 Power consumption is modeled in the following table 10 20 30 40 50 16 27 38 49 60 Machine C: Cookies graph Power consumption graph Cookies Made Power in watts Time in minutes Time in minutes Machine D: Makes approximately 690 cookies in 30 minutes Consumes approximately 90 watts in 30 minutes plus an initial 3 watts to power up the machine 26. Which machine makes cookies the fastest and how do you know? 27. Which machine makes cookies the slowest and how do you know? 28. Which machine uses the most power per minute and how do you know? 29. Which machine uses the least power per minute and how do you know? 30. Which machine uses the least power to turn on (initially) and how do you know? 31. Which machine would use the least total power if it ran for 30 minutes? 32. Which machine would use the least total power if it ran for 10 minutes? 170