Nicholas Zhao Teaches Math

CBE: Algebra Prep

Category focus

Proportionality

Back to bank

Connect slopes, tables, graphs, equations, rates, similar figures, and dilations.

Questions

78

Skill type

proportionality

Study mode

Practice + review

Sample questions

Question

Oscar buys his lunch in the school cafeteria. The cost of 15 school lunches is $33.75. Which graph has a slope that best represents the average cost of the lunches in dollars per lunch? y Lunch Cost y Lunch Cost 18 18 16 16 14 14 12 12 A 10 C 10 8 8 6 6 4 4 2 2 0 123456789 x 0 123456789 x Number of School Lunches Number of School Lunches y Lunch Cost y Lunch Cost 18 18 16 16 14 14 12 12 B D10 10 8 8 6 6 4 4 2 2 0 123456789 x 0 123456789 x Number of School Lunches Number of School LunchesOpen full-size question
  • A.
    Answer A: Answer A (see image)
  • B.
    Answer B: Answer B (see image)
  • C.
    Answer C: Answer C (see image)
  • D.
    Answer D: Answer D (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Figure I and Figure II are similar figures. Figure I Figure II R S A B F W C T E D V U Which proportion must be true?Open full-size question
  • F.
    Answer F: RSAB = TUCD
  • G.
    Answer G: TUAB = UVAF
  • H.
    Answer H: STEF = WRCD
  • J.
    Answer J: WVAB = STEF

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which graph represents y as a function of x? y y 4 4 3 3 2 2 1 1 A C x x −4 4−3 −2 −11 2 3 −4 −3 −2 −1 1 2 3 4 −1 −1 −2 −2 −3 −3 −4 −4 y y 4 4 3 3 2 2 1 1 B D −4 4−3 −2 −11 2 3x −4 −3 −2 −1 1 2 3 4 x −1 −1 −2 −2 −3 −3 −4 −4Open full-size question
  • A.
    Answer A: Answer A (see image)
  • B.
    Answer B: Answer B (see image)
  • C.
    Answer C: Answer C (see image)
  • D.
    Answer D: Answer D (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Triangle HJK and triangle PMK are similar right triangles. The coordinates of all the vertices are integers. y H 1011 9 8 7 6 5 M J K 4 3 2 1 P −1 −11 0 −9 −8 −7 −6 −5 −4 −3 −2 −1 −1 2 3 4 5 6 7 8 9 10 11x 1 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11 Which statement is true about the slope of HK and the slope of PK ?Open full-size question
  • F.
    Answer F: The slope of HK is less than the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for HK than it is for PK .
  • G.
    Answer G: The slope of HK is equal to the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for HK as it is for PK .
  • H.
    Answer H: The slope of HK is greater than the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for HK than it is for PK .
  • J.
    Answer J: The relationship between the slope of HK and the slope of PK cannot be determined, because the triangles are congruent.

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

A bottle contains 30 fluid ounces of orange juice and 18 fluid ounces of pineapple juice. Which graph has a slope that best represents the ratio of orange juice to pineapple juice in this bottle? y Juice y Juice 20 20 16 16 F 12 H 12 8 8 4 4 0 2 4 6 8 10 x 0 2 4 6 8 10 x Amount of Amount of Pineapple Juice (fl oz) Pineapple Juice (fl oz) y Juice y Juice 20 20 16 16 G 12 J 12 8 8 4 4 0 2 4 6 8 10 x 0 2 4 6 8 10 x Amount of Amount of Pineapple Juice (fl oz) Pineapple Juice (fl oz)Open full-size question
  • F.
    Answer F: Answer F (see image)
  • G.
    Answer G: Answer G (see image)
  • H.
    Answer H: Answer H (see image)
  • J.
    Answer J: Answer J (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which graph appears to show a proportional relationship between x and y? y y 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 F H 11 –9 –8 –7 –6 –5 –4 –3 –2 –1 –1 2 3 4 5 6 7 8 9x –9 –8 –7 –6 –5 –4 –3 –2 –1 –1 2 3 4 5 6 7 8 9x 1 1 –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 –7 –7 –8 –8 –9 –9 y y 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 G J 11 –9 –8 –7 –6 –5 –4 –3 –2 –1 –1 2 3 4 5 6 7 8 9x –9 –8 –7 –6 –5 –4 –3 –2 –1 –1 2 3 4 5 6 7 8 9x 1 1 –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 –7 –7 –8 –8 –9 –9Open full-size question
  • F.
    Answer F: Answer F (see image)
  • G.
    Answer G: Answer G (see image)
  • H.
    Answer H: Answer H (see image)
  • J.
    Answer J: Answer J (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which set of ordered pairs represents y as a function of x?Open full-size question
  • A.
    Answer A: ^(0, 0), ( 1, 2), ( 1, 2), ( 2, 4), ( 2, 4)`
  • B.
    Answer B: ^(0, 0), (1, 1), (2, 4), (3, 9), (3, 16)`
  • C.
    Answer C: ^(0, 0), (0, 1), (0, 2), (0, 1), (0, 2)`
  • D.
    Answer D: ^(0, 0), ( 1, 0.5), ( 2, 1), ( 3, 1.5), ( 4, 2)`

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which representation shows y as a function of x? y 5 x y 4 3 2 −11 21 F H1 −1434 −5 −4 −3 −2 −1 −1 2 3 4 5 x 1 −17 47 −2 −3 −20 60 −4 −5 y 5 x y 4 3 2 16 19 G J118 21 −5 −4 −3 −2 −1 −1 2 3 4 5 x 23 1 20 −2 25 −3 22 27 −4 −5Open full-size question
  • F.
    Answer F: Answer F (see image)
  • G.
    Answer G: Answer G (see image)
  • H.
    Answer H: Answer H (see image)
  • J.
    Answer J: Answer J (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which table represents a non-proportional relationship between x and y? A x y C x y 1 −− 4 1 7.5 3 −− 12 4 30 7 −− 28 7 52.5 15 −− 60 10 75 B x y D x y −− 17 93.5 −− 5 11 −− 5 27.5 − −− 1 − 1 2 − 11− 1 − 7− 10 − 55− 8 − 28−Open full-size question
  • A.
    Answer A: Answer A (see image)
  • B.
    Answer B: Answer B (see image)
  • C.
    Answer C: Answer C (see image)
  • D.
    Answer D: Answer D (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Triangle KLM and triangle PRS are similar right triangles. y 12 K 11 10 9 M 87 L 6 5 P 4 3 2 1 −12 −1−11 0 −9 −8 −7 −6 −5 −4 −3 −2 −1 −1 23456789 10 11 12 x 1 −2 −3 −4 −5 −6 −7 S −8 R −9 −10 −11 −12 Which proportion can be used to show that the slope of KM is equal to the slope of PS ?Open full-size question
  • A.
    Answer A: KL PR LM = RS
  • B.
    Answer B: RS LM SP = MK
  • C.
    Answer C: ML SP LK = RP
  • D.
    Answer D: PS KM PR = KL

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which set of ordered pairs represents y as a function of x?Open full-size question
  • A.
    Answer A: (0, 0.5), (2, 1.5), (− 5.5,− − − 5), (− 5.5, − 6)
  • B.
    Answer B: (5, − 7),− − − − − (3, − 7), (− 9.2, − 7), (9.2, − 7)
  • C.
    Answer C: (9.3, − 1),− − (7.3, − 2), (7.3, 2), (9.3, 1)
  • D.
    Answer D: (8.1, 9), (9.1, 10), (10.1, 9), (9.1, 8)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The graph of a linear function passes through the points (1− − −− −, )1 3 and (1, − ). 4 4 y 2 1 −2 −1 1 2x −1 −2 Which equation represents the function?Open full-size question
  • A.
    Answer A: y = 1− −− 2 x − 14
  • B.
    Answer B: y = 12 x + 14
  • C.
    Answer C: y = 1− −− 4 x − 12
  • D.
    Answer D: y = 14 x + 12

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

At a restaurant 600 customers were served during a 10-hour period of time. Which graph has a slope that best represents the number of customers that were served per hour at this restaurant? y Customers y Customers 540 700 480 600 420 500 360 F 400 H 300 300 240 200 180 100 120 x 60 0 1 2 3 4 5 6 7 x Time (hours) 0 1234567 Time (hours) y Customers y Customers 540 70 480 60 420 50 360 G J40 300 30 240 20 180 10 120 x 60 0 1 2 3 4 5 6 7 x Time (hours) 0 1234567 Time (hours)Open full-size question
  • F.
    Answer F: Answer F (see image)
  • G.
    Answer G: Answer G (see image)
  • H.
    Answer H: Answer H (see image)
  • J.
    Answer J: Answer J (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

A linear function is represented on the coordinate grid. y 9 8 7 6 5 5 (0, ) 4 3 2 1 −9 −8 −7 −6 −5 −4 −3 −2 −1 −1 x 1 2 3 4 5 6 7 8 9 −2 −3 (8, −2) −4 −5 −6 −7 −8 −9 What is the y-intercept of the graph of this function?Open full-size question
  • F.
    Answer F: 5
  • G.
    Answer G: 6
  • H.
    Answer H: 7−− 8
  • J.
    Answer J: 8−− 7

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The cost of 6 pencils at a store is 30 cents. Each pencil has the same cost. Which graph has a slope that best represents the cost of each pencil at this store? y Cost of Pencils y Cost of Pencils 45 45 40 40 35 35 30 30 F H25 25 20 20 15 15 10 10 5 5 0 123456789 x 0 123456789 x Number of Pencils Number of Pencils Cost of Pencils Cost of Pencils y y 45 45 40 40 35 35 30 30 G 25 J 25 20 20 15 15 10 10 5 5 0 123456789 x 0 123456789 x Number of Pencils Number of PencilsOpen full-size question
  • F.
    Answer F: Answer F (see image)
  • G.
    Answer G: Answer G (see image)
  • H.
    Answer H: Answer H (see image)
  • J.
    Answer J: Answer J (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Gwen spent $12.50 to purchase 5 bracelets. Each bracelet cost the same amount. Which graph has a slope that best represents this rate? y yBracelets Bracelets 14 14 12 12 10 10 A 8 C 8 6 6 4 4 2 2 0 1 2 3 4 5 6 7 x 0 1 2 3 4 5 6 7 x Number Purchased Number Purchased y yBracelets Bracelets 14 14 12 12 10 10 B 8 D 8 6 6 4 4 2 2 0 1 2 3 4 5 6 7 x 0 1 2 3 4 5 6 7 x Number Purchased Number PurchasedOpen full-size question
  • A.
    Answer A: Answer A (see image)
  • B.
    Answer B: Answer B (see image)
  • C.
    Answer C: Answer C (see image)
  • D.
    Answer D: Answer D (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The graph of a linear function is shown on the coordinate grid. y 9 8 7 (4, 8) 6 5 4 3 2 1 −9 −8 −7 −6 −5 −4 −3 −2 −1 x −1 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 (−5, −7) −6 − − −7 −8 −9 What is the y-intercept of the graph of this function?Open full-size question
  • A.
    Answer A: 2 _3
  • B.
    Answer B: 5 _4
  • C.
    Answer C: 3 _5
  • D.
    Answer D: 3 _4

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The line graphed on the coordinate grid can be used to determine the number of inches of water added to a swimming pool after different numbers of hours. Swimming Pool y 30 27 24 21 18 15 12 9 6 3 x 0 12345 678910 Number of Hours Which statement best describes the slope of the graphed line?Open full-size question
  • F.
    Answer F: The water is being added at a rate of 0.42 inch per hour.
  • G.
    Answer G: The water is being added at a rate of 0.80 inch per hour.
  • H.
    Answer H: The water is being added at a rate of 2.40 inches per hour.
  • J.
    Answer J: The water is being added at a rate of 1.25 inches per hour.

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which situation describes a non-proportional relationship?Open full-size question
  • F.
    Answer F: The circumference of a circle with a radius of x units can be represented by y = 2πx.
  • G.
    Answer G: The perimeter of an equilateral triangle with a side length of x units can be represented by y = 3x.
  • H.
    Answer H: The total surface area of a cylinder with a radius of 1 unit and height of x units can be represented by y = 2πx +2π.
  • J.
    Answer J: The radius of a circle with a diameter of x units can be represented by y = x_1. 2

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which graph does NOT represent y as a function of x? y y 4 4 3 3 2 2 1 1 F x H x −4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4 −1 −1 −2 −2 −3 −3 −4 −4 y y 4 4 3 3 2 2 1 1 G x J x −4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4 −1 −1 −2 −2 −3 −3 −4 −4Open full-size question
  • F.
    Answer F: Answer F (see image)
  • G.
    Answer G: Answer G (see image)
  • H.
    Answer H: Answer H (see image)
  • J.
    Answer J: Answer J (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.