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Coordinate Algebra EOC (GSE) Quiz Answer KeyInterpreting Categorical and Quantitative Data - (MGSE9‐12.S.ID.7 ) Interpret Slope

Student Name: _______________________ Date: _________Teacher Name: THUYNGA DAO Score: _________

1)

Suppose an airplane climbs 15 feet for every 40 feet it moves forward. What is the slope of this airplane's ascent?

A)- 3

8

B)- 8

3

C)1

3

D)3

8

Explanation:

The slope of the airplane's ascent is 3

8. Slope is rise over run, so

15

40 =

3

8.

2) Cathy pays $25 a month plus $0.05 per text message. She models this with the function C = 0.05x + 25. If the text messaging feeincreases to $0.10, what is her new function?

A) C = 10x + 25

B) C = 0.10x + 25

C) C = 0.10x + 0.05

D) C = 0.05x + 0.10

Explanation:The monthly fee is the y-intercept and the text messaging fee is the slope. The correct answer is C = 0.10x + 25.

3) Greg sells cars. He makes a base salary of $25,000, plus $1500 per car he sells. The function that models this situation is S =1500x + 25000. After working at the car dealership for 2 years, he gets a raise. He now makes $1700 per car he sells. What is thenew function that models this situation?

A) S = 1700x + 1500

B) S = 1500x + 1700

C) S = 1700x + 25000

D) S = 25000x + 1700

Explanation:The base salary is the y-intercept and the money Greg makes per car is the slope. The correct answer is S = 1700x + 25000.



4) In the function y = 0.25x + 3.5, y represents the cost of a gallon of milk after a certain number of years, x. How much does the costof milk increase every year?

A) $0.07

B) $0.25

C) $0.60

D) $14

Explanation:The slope is the coefficient in front of x. Since the slope of the equation is 0.25, the cost of milk increases $0.25 a year.

5)

W = pt + 105

A wrestler is trying to gain weight for an upcoming match. His current weight is 105. In the formula shown, W = weight, p = poundsand t = time(weeks). He has 6 weeks before his match and has a goal weight of 123 pounds. Determine the minimum number ofpounds he must gain per week to meet his goal.

A) 1 pound

B) 2 pounds

C) 3 pounds

D) 4 pounds

Explanation:The solution is 3 pounds. He currently weighs 105 pounds and must gain 18 pounds to meet his goal. If we spread this over 6 weeksthat is 3 pounds per week.



6)

A pizza parlor sells a basic cheese pizza for $6. There is a charge to add additional toppings. Based on the graph, determine the priceper topping.

A) $0.25

B) $0.50

C) $0.75

D) $1

Explanation:

The solution is $0.50. The slope of the graphed line is 1

2. Therefore, the cost of each additional topping is $0.50.

7) The population, in millions, of a city t years after 1990 is given by the equation P(t) = 2.9 + 0.08t. In this function,

A) 0.08 million is the population of the city in 1990 and 2.9 million is the increase per year in the population.

B) 2.9 million is the population of the city in 1991 and 2.98 million is the population in 1992.

C) 2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population.

D) 2.9 million is the population of the city in 1990 and 0.08 million is the decrease per year in the population.

Explanation:2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population. The figure 2.9 doesn'tchange, but the population grows by 0.08 million each time t increases.



8) A high school chorus has $1000 in its school account at the beginning of the year. They are putting on a fall concert to raisemoney for a trip later in the year. At the concert last year they sold tickets for $10 each. If they sell tickets at the same price the totalamount in the chorus account can be represented by the linear function T = 10x + 1000. If they increase the ticket price to $15, howmany tickets will they have to sell to have a total of $4000 in the account?

A) 100 tickets

B) 150 tickets

C) 200 tickets

D) 250 tickets

Explanation:The solution is 200 tickets. With a slope of $15, and $1000 already in the account, the chorus must sell 200 tickets to reach the goalof $4000.

9) Chris has $100 in his savings account and he adds $20 a month to the account. The total amount can be represented by the linearfunction T = 20x + 100. His goal is to have a total of $300 in four more months. What should he change in the function to reach thisgoal?

A) Change the amount he adds each month to $50.

B) Change the amount he adds each month to $40.

C) Change the y-intercept of the linear function to $20.

D) Change the y-intercept of the linear function to $50.

Explanation:Change the slope or amount he adds each month to $50. With a slope of $50, Chris will add $200 to his account over 4 months. Thiswill give him a total of $300 in the account.

10)

The graph shows how many sandwiches can be made from different numbers of loaves of bread. What is the slope of the graph?

A) 10

B) 5

C)1

20

D)1

10

Explanation:Slope can be thought of many different ways that all give the same value. It’s the change in y per change in x. You get 10 moresandwiches for each new loaf. It’s also equal to k in y = kx. The graph here is for y = 10x; its slope is 10.



11)

Brent is trying to figure out the relationship between the number of times his friends post on social media and their grade pointaverages. He records the collected data on a scatter plot. Which correlation exists between the GPA and the number of social mediaposts?

A) no correlation

B) cannot be determined

C) weak positive correlation

D) strong negative correlation

Explanation:strong negative correlation

The GPA represented by y, the dependent variable, decreases as the number of posts, represented by x, the independent variable,increases.



12) Jessie owns a hot dog stand and sells specialized hot dogs. He charges $1.50 for a plain hot dog and then an additional $0.50 foreach topping that you want. This can be modeled by the equation C = .5x + 1.5, where C is the total cost of the hot dog and x is thenumber of toppings you ordered. The company that he buys his hot dogs from was having a sale so he was able to buy the hot dogsfor less. He will now sell them for $0.25 less than before. What should be changed in the equation C = .5x + 1.5 to represent this?

A) Replace the .5 with a .75

B) Replace the .5 with a .25.

C) Replace the 1.5 with a 1.25

D) Replace the 1.5 with a 1.75

Explanation:In the equation C = .5x + 1.5, the .5 is the cost of each additional topping and the 1.5 is the basic cost of the hot dog. Since he is ableto reduce the cost of the hot dog by $0.25 he needs to Replace the 1.5 with a 1.25

13) A school club is raising money for a trip, and needs to reach $10,000. Their fundraising progress is modeled by the function

f(x) = 435 + 1200x, where x is measured in weeks.

What is the meaning of the constant 435?

A) It is the amount they started with.

B) It is the amount still to be raised.

C) It is the amount which is left over.

D) It is the amount they raise each week.

Explanation:It is the amount they started with. This is the y-intercept, so it is the amount of money that had at time zero, which is when theystarted.

14)

How many inches does the ramp rise for each inch of length? Round to the nearest hundredth.

A) .25 inches

B) .33 inches

C) .34 inches

D) .67 inches

Explanation:The solution is .33 inches. The solution is found by calculating the rate of change. The rate of change is 1/3 or approximately .33.



15) Mrs. Mitchell decided to grade her projects by giving each student 50 points if they turned in a project and then an additional 5points for each part they got correct. After looking through some of the projects, she decided to give the students 7 points for eachcorrect section. If Mrs. Mitchell wrote a function to describe the situation, what would change?

A) the slope

B) the y-intercept

C) both the slope and y-intercept

D) the function would remain the same

Explanation:The base 50 points for a completed project is the y-intercept and the points given for correct sections is the slope. Since it was thepoints given for each correct section that changed, it was the slope that changed.

16) The tooth fairy brings Jack $5 plus $1 for each tooth that he loses. After Jack loses a few teeth, the tooth fairy decides that he ispaying too much money for teeth. He now gives Jack $5 plus $0.50 for each tooth lost. Which graph shows the new function?

A)



B)

C)



D)

Explanation:The $5 is the y-intercept and the $0.50 per tooth is the slope. The correct answer is graph B.

17) Georges asked five of his friends how long they studied for the last math test and what grade they received. He found a linearregression equation for the data to be y = 9.6x + 65.8. What does the 9.6 mean in the context of this equation?

A) His friends on average studied 9.6 hours.

B) If they studied 9.6 hours they would get a 0 on the test.

C) They should study 9.6 hours in order to get an A on the test.

D) For every hour they studied their grade would go up 9.6 points.

Explanation:The 9.6 is the slope in the equation so it is going to be a rate of change. Since the grade they received on the test is the outputvalues and the amount of time they studied are the input values the 9.6 means That for every hour they studied their grade wouldgo up 9.6 points.



18) A science class is tracking the progress of plant growth. The class starts the experiment with a plant five centimeters high. Theplant grows two centimeters each day. The model for plant growth "y" is given by: y = 2x + 5. What is the meaning of the y-interceptin this equation?

A) the y-intercept is the starting date

B) the y-intercept is two times larger than five

C) the y-intercept is the starting height of the plant

D) the y-intercept is the largest height the plant can grow

Explanation:The y-intercept is the starting height of the plant is correct. In the model y = 2x + 5, To find the y-intercept, x = 0; thus y = 2(0) + 5; y= 5. 5 cm was the starting height of the plant.

19)

Find the slope of ED.

A) -1

B) 0

C) 1

D) undefined

Explanation:0 ED is a vertical line. The slope of any horizontal line is undefined.

20) Managers at a company rate employee's on performance and attitude and find that an employee's attitude depends on theirperformance. They find a linear relationship and the line of best fit is y = 11.7 + 1.02x. What does 1.02 mean in the context of theproblem?

A) That if their attitude rating was 0 the performance rating would be 1.02.

B) That if the performance rating was 0, their attitude rating would be 1.02.

C) That for every point their performance rating goes up their attitude rating improves by 1.02 points.

D) That for every point their attitude rating goes up their performance rating improves by 1.02 points.

Explanation:Since 1.02 is the slope then the meaning is That for every point their performance rating goes up their attitude rating improves by1.02 points.

21) Joseph owns a hot dog stand and sells specialized hot dogs. He charges $1.50 for a plain hot dog and then an additional $0.50for each topping that you want. This can be modeled by the equation C = .5x + 1.5, where C is the total cost of the hot dog and x isthe number of toppings you ordered. Hattie sells hamburgers at the stand next door and has the same basic cost except she charges$2.50 for a plain hamburger and then $0.25 for each additional topping. How should she change Joseph's cost equation to representher hamburger cost?

A) Replace the .5 with a .25.

B) Replace the 1.5 with a 2.5

C) Switch the x and C.

D) Replace the .5 with a .25 and the 1.5 with a 2.5

Explanation:



In the equation C = .5x + 1.5, the .5 is the cost of each additional topping and the 1.5 is the basic cost of the hot dog. Since Hattiecharges different amounts for both of these she needs to Replace the .5 with a .25 and the 1.5 with a 2.5.



22)

What is the slope of the line?

A) 1

B) 6

C) 8

D)1

2

Explanation:8

Substitute two points on the line into the slope formula.

m = y2 - y1

x2 - x1

Using (80, 10) (90, 90):

m = (90 - 10)

(90 - 80)

m =80

10 = 8

23) A small company did an analysis of their pay scale versus years of experience and found that the line of best fit was y = 2035.6x+ 36,000. What does the 2035.6 mean in context of the problem?

A) That employees on average earn $2035.60 per year.

B) That if they had 2035.6 years of experience they would earn $0.



C) That they should have 2035.6 years of experience in order to earn the most money.

D) That for every year of experience they have their salary would increase by $2035.60.

Explanation:The 2035.6 is the slope in the equation so it is going to be a rate of change. Since the salary they earn is the output values and theyears of experience are the input values the 2035.6 means That for every year of experience they have their salary would increaseby $2035.60.

24) A small company did an analysis of their pay scale versus years of experience and found that the line of best fit was y = 2035.6x+ 36,000. What does the 36,000 mean in context of the problem?

A) That the lowest salary anyone could earn was 36,000.

B) That if they had 0 years of experience their salary would be 36,000.

C) That currently the lowest salary of any employee in the company was 36,000.

D) That for every year of experience they had their salary would go up 36,000.

Explanation:The 36,000 is the y-intercept of the equation and therefore the x-value must be 0. Since the salary they earn is the output values themeaning is That if they had 0 years of experience their salary would be 36,000.



25) Rob is saving money for a down payment on a house. He opens a savings account at his local bank and deposits $1000. Hemodels his savings plan with the equation y = 400x + 1000 based on his current income and monthly savings rate. What is themeaning of the y-intercept in the equation?

A) largest amount that he can save

B) date when he will have enough saved

C) date his savings account was started

D) starting amount in his savings account

Explanation:The y-intercept represents the starting amount in his savings account.

x = 0 for the y-intercept.

y = 400x + 1000y = 400(0) + 1000y = 1000

26)

Find the slope of EF.

A) -1

B) 0

C) 1

D) 2

Explanation:0 EF is a horizontal line. The slope of any horizontal line is 0.

27) Eric sells shirts. It costs him $100 to buy all the shirts and $10 to print designs on the shirts. Eric sells each shirt for $4. So farEric has sold 20 shirts. Eric uses an equation to calculate his total profit.

What is the slope of the equation modeling this situation?

A) 4

B) 10

C) 20

D) 40

Explanation:4 is the coefficient. Eric's equation is Profit = 4x - (100 + 10).The coefficient is 4.

28) Managers at a company rate employee's on performance and attitude and find that an employee's attitude depends on theirperformance. They find a linear relationship and the line of best fit is y = 11.7 + 1.02x. If the performance rating increased by 2points what would happen to the attitude rating?

A) It would increase by 2.04 points.

B) It would increase by 11.25 points.



C) It would increase by 23.4 points.

D) It would increase by 0.089 points.

Explanation:Since performance is the independent variable then each increase by one point results in a 1.04 increase in the attitude rating.Therefore, the attitude rating would increase by 2.04 points.



29) Profit is equal to the revenue obtained from selling items minus the cost of producing those items, i.e. P(x) = R(x) – C(x) where xis the number of items produced. If C(x) = 0.5x + 3 and R(x) = 2.5x, what should the production level, x, be to generate a profit of$99?

A) 50

B) 51

C) 52

D) 53

Explanation:51 is correct. Since P(x) = R(x) – C(x), 2.5x – (.5x + 3) = 2x – 3 = 99, so x =51.

30) Georges asked five of his friends how long they studied for the last math test and what grade they received. He found a linearregression equation for the data to be y = 9.6x + 65.8. What does the 65.8 mean in the context of this equation?

A) If they studied 0 hours they would earn a 65.8.

B) The lowest grade of his five friends was a 65.8.

C) The lowest grade they could receive on the test was a 65.8.

D) For every hour they studied their grade would go up 65.8 points.

Explanation:The 65.8 is the y-intercept of the equation and therefore the x-value must be 0. Since the grade they received on the test is theoutput values the meaning is That if they studied 0 hours they would earn a 65.8.

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