Georgia Online Formative Assessment Resource (GOFAR) G8 …chambleems.dekalb.k12.ga.us/Downloads/G8-Q2-ALG...A man lowers a lobster trap below the ocean’s surface at a constant rate

G8-C-ALG-Q2-49

Name:____________________________

Date: ____________________________

Georgia Online Formative Assessment Resource (GOFAR)

Copyright © 2015by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 38 )

1. The equation shown represents the relationship between two quantities.

Part AWrite a situation to represent each part of the equation. Be sure to identify which quantity corresponds to each variable in the equation.

Part BCreate a set of 5 ordered pairs for the given equation.

Part CIs the given equation a function? Explain your answer.

Be sure to complete ALL parts of the task.Write your answer and show your work on the paper provided.

Do NOT type your answer in the text box below.

2. Each of the graphs shown represents a different situation.

Part AWhich graph shows the temperature of a pizza after it is put into an oven to bake? Explain your reasoning, including the label for eachaxis.

Part BWhich graph shows the amount of gas in the tank of a truck driving at a constant speed on a level road? Explain your reasoning,including the label for each axis.

Part CWhich graph shows the height of a ball from when it is thrown to the time is hits the ground? Explain your reasoning, including thelabel for each axis.

Part DWrite a situation that could be represented by the graph not used in Parts A, B, or C. Explain your reasoning.





3. Use the table shown to answer each part.

Part AWrite two additional ordered pairs that would be a part of the same function as shown in the table.

Part BWrite a function to represent the relationship between the x - and y -values as shown in the table. Describe what each part of thefunction you wrote represents with respect to a graph of the function.

Part CWhat would the graph of the values shown in the table look like? Explain your answer.





4. Liam used the equation shown to create a sequence where represents the first term in the sequence.

Part ACreate a table to represent the first 5 terms of the sequence.

Part BLiam says the equation can be used to represent a functional relationship. Explain whether or not Liam’s statement is true.

Part CMartha attempts to graph the equation Liam used to create a sequence. Her graph of the equation is shown below.

Martha says the equation Liam used for the sequence represents a linear relationship. Martha is incorrect.●Write the equation that represents Martha’s graph. Explain whether or not Martha’s graph represents a linear relationship.●Explain the error Martha made when creating the graph of the equation Liam used to create a sequence.



5. A biology teacher gave three students in his class a different plant. He asked the students to record the



heights of their plants, in centimeters (cm), everyday for one week. The students reported their results indifferent displays. Their results are shown in a graph, an equation, and a table.

Part AList the plants in order from the slowest rate of growth per day to the greatest rate of growth per day.Explain how you got your answer.

Part BIf the growth rate for Plant 1 remains the same, on what day number will it be 24 cm tall? Explain how yougot your answer.

Part CIf the growth rate for each plant remains the same, when will Plant 2 and Plant 3 be the same height?Show work or give an explanation to justify your answer.



6. Parts A, B, and C each present a pair of linear equations. Without graphing the equations, determinewhether the graphs of each pair of lines would intersect. Explain how you know whether the lines wouldintersect or not.



Part A

Do the graphs of Line 1 and Line 2 intersect? Explain how you know without graphing the lines.

Part B


Part C




7. The coordinate grid shows the reading rates of Justin and Nadia during a reading program at school.



Part ABased on the graph, how long will it take Nadia to read 1 book? Explain your answer.

Part BIf Justin’s reading rate stays the same, how many books will Justin read in two weeks? Explain youranswer.

Part CBased on the graph, what does the y -intercept for Nadia’s reading rate represent?

Using the graph, compare the y -intercept for Justin’s reading rate to the y -intercept for Nadia’s readingrate. Explain your answer.

Part DRafael is also in the reading program with Nadia and Justin. The table shows Rafael’s reading rate over aperiod of six weeks.

Write a function to represent Rafael’s reading rate as shown in the table. Show your work.

Who has the greatest reading rate (Justin, Nadia, or Rafael)? Explain your answer.





8. The graph shows the relationship between the volume of Liquid 1 and its mass.

Part AWrite the equation of the line that represents the graph of Liquid 1. Explain the meaning of the coefficientin the equation you wrote to the graph of Liquid 1.

Part BThe equation is used to represent the relationship between the volume of Liquid 2 and its mass.Explain how the graph of Liquid 1 is similar to the graph of Liquid 2. How are the graphs different?

Part CUsing the graph for Liquid 1, explain how you can use the point to determine the value of gin thepoint What is the value of g ?



9. A given function is defined by the equation



Part ADoes the equation define a linear function? Explain your answer.

Part BTwo functions are considered parallel if their slopes are equivalent.

Write the equation for a function that is parallel to the given function with a y-intercept of Explain theequation you wrote.

Part CWrite the equation for a function that represents a proportional relationship and is also parallel to the givenfunction. Explain the equation you wrote.



10. Triangle EGH is graphed on a coordinate grid.

Part AUsing the Pythagorean theorem, determine the length of side Show your work.



Part BWhat is the slope of the line containing What is the slope of the line containing Explain therelationship between the slopes of and

Part CWrite an equation to represent the line that passes through points E and G .

If in the equation you wrote, what is the value of y ? Show your work.



11. Use the coordinate grid shown to answer Parts A and B.

Part AList three ordered pairs that are part of the same linear function. Explain your answer.

Write the equation for the function which contains these points.

Part B



Graph the points and on the coordinate grid. Are the points linear or nonlinear?Explain your answer.



12. The equation represents the depth, in feet, of a submarine diving below the ocean’s surface,where d represents the depth and t represents the time, in minutes.

Part AA man lowers a lobster trap below the ocean’s surface at a constant rate of 30 feet per minute. How doesthe rate of change of the lobster trap compare to the rate of change of the submarine? Explain youranswer.

Part BAt what time does the lobster trap begin its descent? How many feet is the lobster trap below the ocean’ssurface at this time?

Part CWrite an equation representing the depth, in feet, of the lobster trap in terms of the time.

Part DWill the graphs of these two functions intersect? Explain your answer.





13. Three packaging companies use the expressions shown to calculate the cost, in dollars, for shipping anitem weighing x pounds.

Company R:

Company S:

Company T:

Part AFor what weight will the cost be the same for Company R and Company S? Show your work.

Part BFor what weight will the cost be the same for Company S and Company T? Show your work.

Part CWhich company has the highest rate? Explain your answer.

Part DAvery says it is less expensive to ship an item using Company S than Company R. Is Avery correct? Explainyour answer.



14. Jenn and Mara are playing a computer game in which a player receives x points for every correctdecision and loses y points for every incorrect decision.

●Jenn made 18 correct and 12 incorrect decisions for a total of 39 points.●Mara made 16 correct and 8 incorrect decisions for a total of 36 points.

Part AWrite two linear equations in x and y to represent Jenn’s and Mara’s situation.

Part BSolve the system of linear equations from Part A algebraically. Show your work.

Part CWhat are the coordinates of the point of intersection of the graphs of these two lines? Explain your answer.



Part DDescribe in words the significance of the point of intersection in this context.



15. Four friends want to rent a rock-climbing facility for a party. They agree to share the cost equally. Therental charge is n dollars per hour regardless of how many people are using the facility.

Part AWrite an expression, in terms of n , that represents the cost per person for the four friends to rent thefacility for two hours.

Part BAnother friend agrees to join in renting the rock-climbing facility for two hours. The fifth friend will alsoshare the cost equally. Write an expression, in terms of n , that represents the difference in the cost perperson if five people share the rental charge. Explain your answer.

Part CThe difference in the cost when 5 people share the cost to rent the facility for two hours and when only 4people share the cost to rent the facility for two hours is $18.75 per person. Write an equation, in terms of n , that models this situation. Solve the equation for n , and explain what the value you find for nrepresents. Show your work.

Part DAfter the first two hours, the rock-climbing facility charges $120 per hour if the customer wants to extendthe party time. Let x represent the total number of hours for the party and y represent the customer’s totalcost. Write a function that expresses the linear relationship between these two variables. Explain youranswer.





16. Lines m and n are graphed on a coordinate grid.●Line m has a slope of 2 and a y-intercept of

●Line n has a slope of 3 and a y -intercept of 2.

Part AWrite the equation that represents line m .

Write the equation that represents line n .

Part BUsing the equations you wrote in Part A, find the point where lines m and n intersect. Show your work.

Part CWrite the equation of a line that passes through both the intersection point found in Part B and the origin.Explain your equation or show your work.



17. Amber and Michael recorded the length and weight of each catfish they caught while on vacation in 2012. The scatter plotshows their results.

They also created the table shown below to record the number of catfish they caught while on vacation over the past fiveyears.



Part ADoes the scatter plot describe a function? Explain your answer.

Part BDo the values shown in the table describe a function? Explain your answer.

Part CAmber and Michael’s parents caught twice as many catfish during every vacation. If x represents thenumber of catfish that Amber and Michael caught, and y represents the number of catfish caught by theirparents, write an equation that models this relationship.

Does this equation describe a function? Explain your answer.



18. The graph represents the wages a call center pays its entry-level employees, where y is the total wagespaid per hour for x employees.



Part ACalculate the unit rate from point J to point K, the unit rate from point K to point R, and the unit rate frompoint R to point S. Show your work. What conclusion can be made about points J, K, R, and S?

Part BA grocery store is filling entry-level management positions. The store pays $13.25 per hour for eachemployee. Write an equation representing this situation.

Part CA job seeker inquires about the hourly wages paid at the call center and at the grocery store. She decidesto apply for the job that pays more per hour. For which job should the job seeker apply? Explain youranswer.



19. A class is studying linear equations.

Part AGive an example of a linear equation to represent each type of solution set:

●A linear equation with exactly one solution



●A linear equation with infinitely many solutions

●A linear equation with no solutionsFor each example, explain why the equation has that number of solutions.

Part BWhat is the solution set for the equation Show your work.



20. A student is working with the two functions shown.●

●The second function is the set of all values when the input value is multiplied by 5.Part AThe student does not understand what a function is in terms of inputs and outputs. Write an explanation forthe student.

Part BWhich function has the greater y-intercept? Show your work and explain your answer.





21. Hector works 12.5 hours per week at a part-time job. His original pay rate was $8 per hour, but hereceived a raise of x dollars per hour. His new total weekly pay, y, is represented by the equation

Part AIf what was the amount of Hector’s raise per hour? Show your work.

Part BWhat are the slope and y-intercept of the equation

Write the equation of a line, in form, that has the same slope and a y-intercept that is 10 unitsmore than the graph of Explain your answers.

Part CJamal’s new weekly pay is given by the equation where y is the total pay in dollars. What isthe solution to the system of equations and Show your work or explain youranswer.



22. Use the equation shown to answer each part.

Part AIf is the equation above a linear function of x? Explain your answer by using an equation solvedin terms of y. Show your work.

Part BWhat is the solution of the given equation when Show your work.

Part CDoes the equation have a solution if Explain your answer.





23. The graph shows the temperature over a 12-hour period.

Part AWhy does this graph represent a function? Explain your answer.

Part BThis graph shows a “piecewise function” because it can be defined with different function rules overdifferent input intervals. What are the two input intervals of the function? What type of function rule can beused to describe the graph in each interval?

Part CAnalyze the graph to describe where the function is increasing or decreasing. Include how the graph differsin the two input intervals of the function in your analysis. Justify your answer.

Part DWrite an equation for a single linear function that includes both endpoints of the graph. Show your work.





24. Haley has the option of 2 different weekly pay rates. Let x be the number of hours she works and let ybe the total amount of money, in dollars, she earns.

Part AHaley is paid using Pay Rate 1. She earns $317.25 per week. How many hours per week does Haley work?Show or explain your work.

Part BWhat ordered pair represents the intersection of the graphs for these two pay rates? Show your work.Explain what the ordered pair represents in the context of the problem.

Part CHaley is offered a new pay rate, Pay Rate 3. Pay Rate 3 does not have any solutions in common with PayRate 2. Give a possible equation for this new pay rate, ydollars, in terms of x, the number of hours worked.Explain why your equation is a possible representation for Pay Rate 3.



25. The function represents the total cost, y dollars, of buying x tickets to a concert.

Part AWhat type of function is this? Explain your answer by identifying the parts of the equation that representthe characteristics of this type of function.

Part BEllen’s total cost for tickets to the concert is $86. How many tickets did Ellen buy? Show your work.

Part CHow could this function be changed to represent a proportional relationship with a steeper slope? Explainyour answer.





26. The diagram shows two stacks of plastic cylinders and their total heights. The diameters of the cylinders used within thestacks are the same length.

Part AThe shaded cylinders are each x feet tall, and the unshaded cylinders are each y feet tall. Write anequation, using x and y, to describe the height of Cylinder G and an equation, using x and y, to describethe height of Cylinder H.

Part BWhat are the values of x and y? Show your work.

Part CSuppose that both equations you wrote in Part A are graphed on the same coordinate grid. Describe whatthe graphs of the equations would look like.

Part DWhat is the connection between the graphs you described in Part C and your answers in Part B?



27. The graphic shows some guidelines a fitness trainer has posted in a gym.



Part AWrite an equation that represents the maximum heart rate, y, as a function of a person’s age, x.

Does the equation you wrote represent a linear or nonlinear function? Explain your answer.

Part BWrite an equation that represents the target heart rate during low intensity exercise, y, as a function of aperson’s age, x.

Does the equation you wrote represent a linear or nonlinear function? Explain your answer.

Part CCompare the two functions you wrote in Part A and Part B. Which function has the greater rate of changeas a person ages? Explain your answer.

Part DMaria is 30 years older than her daughter Beth. What is the difference, in beats per minute, betweenMaria’s target heart rate and Beth’s target heart rate? Explain your answer.



28. The function estimates the area, A square inches, of a circle with radius r inches.

Part AUse the formula to determine the value of A for and Show your work.

Part BDraw a first-quadrant coordinate grid, where the horizontal axis represents the radius and the vertical axisrepresents the area of the circle. Plot the points for the function that you found in Part A.

Part CIs this function linear or nonlinear? Explain your answer.





29. The table shows the proportional amounts of cranberry juice and apple juice used to make Fruit Punch A.

Part AUse the values shown in the table to write an equation for Fruit Punch A that represents the relationshipbetween y, the number of ounces of apple juice, and x, the number of ounces of cranberry juice. Showyour work or explain your answer.

Part BWhat part of the equation you wrote in Part A represents the unit rate? Explain why it represents a unitrate.

Part CGraph the equation from Part A. How does the graph reflect what you described in Part B?

Part DFruit Punch B uses 2.2 ounces of apple juice for every ounce of cranberry juice. How would a graphrepresenting the relationship between the number of ounces of apple juice and the number of ounces ofcranberry juice in Fruit Punch B differ from your graph in Part C? Explain your answer.





30. Two relations are given in different formats.

Use these relations to answer the questions.

Part ADetermine whether or not each relation represents a function. Justify your answers.

Part BDetermine whether each function identified in Part A is linear or nonlinear. Explain how you know.

Part CWrite an equation for each linear function identified in Part B. Explain what each part of your equation(s)represents.



31. The graph and table show the distance and time that Ravyn ran on two different days.



Part AGraph the data for Ravyn’s Tuesday run. Be sure to label your axes and give a title for your graph.

Part BWhat is Ravyn’s rate for each run? Explain how you calculated the rate of each run.

Part CRavyn represents Sunday’s and Tuesday’s runs as a system of linear equations. Write the system of linearequations that represents Sunday’s and Tuesday’s runs, where x represents time and y representsdistance.

Part DWhat is (are) the solution(s) to the system of linear equations you wrote in Part C? Show your work.Explain the meaning of the solution(s).



32. Jon is going to get a job as a delivery driver. He can choose between the two plans shown for his weeklysalary. Let x represent the number of hours Jon works in a week and let y represent his weekly salary, indollars.



Part AWhich plan has a greater rate of change? Show or explain your work.

Part BWhich plan has the greater pay for 15 hours worked in a week? Show or explain your work.

Part CFor what number of hours worked in a week would Jon earn the same weekly salary under either plan?How much would Jon earn during this week? Show or explain your work.



33. Students are given a pass code to access their school library accounts. The pass codes consist of 2 two-digit numbersseparated by an underscore. For example, Amy’s pass code is 30_15.

Part AMario gave two clues about his pass code.

● If the second number is subtracted from the first number, the difference is 15.

●The sum of the first number and the second number is 61.What is Mario’s pass code? Show your work.

Part BLynne’s pass code is the point at which the lines, represented by the equations shown, intersect.

She explained that the x-coordinate was the first number of her pass code and the y-coordinate was the second number.What is Lynne’s pass code? Show your work.



Part CRecall that Amy’s pass code is 30_15. Create a system of two linear equations, both involving x and y, such that its solutiongives Amy’s pass code. Let and Show your work.



34. Josh is working with functions in his mathematics class.

Part AJosh compares two functions. One function is represented by the equation and the otherfunction is represented by the values shown in the table below.

Which function has a greater y-intercept? Show and explain your work.

Part BJosh wrote an equation to represent the function shown in the graph below.



Write the equation of a function that has a rate of change 3 times greater and has the same y-intercept asthe function shown in the graph. Show and explain your work.



35. The coordinate grid shows the graph of a function.



Part AExplain where the graph of the function is decreasing and increasing.

Part BSketch a function that passes through the points and and which increases when

and decreases when Explain your graph.



36. A function increases from to 2 along the x-axis and then decreases from 2 to 8 along the x-axis.

Part ASketch a graph of the function on a coordinate grid. Explain the y-values of the function you sketched.

Part BExplain a characteristic about your graph that shows why it is a function.

Part CIs your graph linear or nonlinear? Explain your answer.

Be sure to complete ALL parts of the task.



Write your answer and show your work on the paper provided.Do NOT type your answer in the text box below.

37. Jason's teacher proposed a system of equations relating to a bicycle race where Pamela rode at twodifferent speeds. Jason needed to solve the system of equations shown.

In the equations, x represented the number of hours Pamela bicycled at a slower average speed, and yrepresented the number of hours Pamela bicycled at a faster average speed.

Part AJason's work for solving the system of equations is shown below.

Jason made at least 1 error. Identify each step in which Jason made an error and explain each error. (Giveonly those errors that are made based on the previous step.)

Part BSolve the system of equations algebraically. Show your work.

Part CSketch the graph of the system. Explain what the solution to the system of equations represents withrespect to the graph of the system.

Part DExplain what the solution to the system of equations represents in the context of the problem.





38. Jacob is comparing two washing machine models at a store. One of the models operates at the speedshown in the table.

A second model completes rotations in 20 minutes.

Part AHow many rotations does the second washing machine complete in one minute? Show your work.

Part BWrite the equations to model the number of rotations, y, made by each washing machine in x minutes.

Part CBased on the equations derived in Part B, how many more rotations will the faster washing machinecomplete than the slower machine in 24-minute washing cycles? Show your work and explain your answer.





39. What is the solution to

Type your answer in the box.You may use numbers, symbols, and/or text in your answer.

40. Describe one characteristic that is the same about both of the two systems of equations shown.




41. A library charges fines for late returns on audio materials. The fine, in dollars, is the same each day. Theordered pairs and represent the corresponding days, x, and fine charges, y. What is the rateof change of the function expressed as a unit rate?


42. The graph shows the amount of water in a large tank as it was filled and drained at different pointsthroughout a 10-hour period.

According to the graph, for how many hours did the amount of water increase?




43. Anna and Frank are comparing the percentages of their laptops' batteries charged over time. Anna'slaptop is currently 60% charged. Every 10 minutes it uses 8% of its battery charge. The graph showsFrank's laptop battery when fully charged and the percent remaining after time in minutes.

Based on the information, what is the difference in the amount of time it takes the two batteries to reach acharge of 0?


44. In order for the graph of the equation to be a linear, what must be the value of n?




45. The table shows the charges from a courier service company for transporting documents depending onthe distance, in miles, of the delivery.

Write a function to model the relationship between x, the distance of the delivery, and c, the total cost ofthe service.


46. On the coordinate plane below, is the image of after 2 translations.



Explain why A, D, and G are collinear.


47. The table shows inputs and outputs for a relation.

Explain what missing value of x would make the relation shown in the table NOT a function.




48. A relation is graphed in the coordinate plane.

Explain whether the graph represents a function over the domain


49. The graph shows the relationship between the number of songs, x, that Gary downloaded and the totalcost, y, of the songs.



What is the unit rate shown in the graph?




Documents

Georgia Online Formative Assessment Resource (GOFAR) G8 …chambleems.dekalb.k12.ga.us/Downloads/G8-Q2-ALG...A man lowers a lobster trap below the ocean’s surface at a constant rate