Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.2Analyze Graphs of Relationships Between Two Variables

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use a table and a graph to determine and analyze the relationship between two variable quantities.

Why This Matters The ticket shows the cost to attend a college football game. How does the total cost of tickets relate to the number of tickets purchased?

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
graphSpanish: gráfica A picture on a coordinate plane that shows how two quantities are related. points that rise in a line
table of valuesSpanish: tabla de valores A list of matched pairs of values that shows a relationship using numbers. months 1, 2, 4 beside cost 24.95, 49.90, 99.80 — one row per pair.
ordered pairSpanish: par ordenado Two numbers written as (x, y) that name one point on a graph. The independent variable comes first. (3, 12)
axisSpanish: eje One of the two number lines that frame a graph. Each axis is labeled with a quantity from the problem. x-axis and y-axis
coordinatesSpanish: coordenadas The numbers in an ordered pair that tell how far to move along each axis to reach a point. x-coordinate, y-coordinate
Rate of changeSpanish: Tasa de cambio How much y changes each time x goes up by one. Up $4 for each hour.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A table for y = 4x has x = 1, 2, 3. Plot the points.

  1. Write the pairs: (1, 4), (2, 8), (3, 12).
  2. Plot (1, 4): right 1, then up 4. Plot the others the same way.
  3. Check: the points line up.

Answer: three points in a straight line

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

The tram travels 1,200 feet every minute. Which quantity is independent — time or distance?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The independent variable is , so it goes on the axis.
  • The ordered pair ( , ) means that .
  • To plot a point I move first, then .
  • As x increases, y , so the points .

Word bank graphordered paircoordinatesaxisplotpointtableinputoutputrateincreasesorigin

Watch out!A common mistake

Reversing the coordinates of a point

Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.2Analyze Graphs of Relationships Between Two Variables

Level 0Most support · every hint printed

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can use a table and a graph to determine and analyze the relationship between two variable quantities.

Why This Matters The ticket shows the cost to attend a college football game. How does the total cost of tickets relate to the number of tickets purchased?

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A table for y = 4x has x = 1, 2, 3. Plot the points.

  1. Write the pairs: (1, 4), (2, 8), (3, 12).
  2. Plot (1, 4): right 1, then up 4. Plot the others the same way.
  3. Check: the points line up.

Answer: three points in a straight line

  1. 1Circle the letter of the best answer. Show how you know.

    Football tickets cost $45 each. What is the total cost of 3 tickets?

    1. A$45
    2. B$48
    3. C$90
    4. D$135
    Steps to try
    1. What is the cost of ONE ticket?
    2. Each of the 3 tickets adds another $45.
    3. Multiply the price of one ticket by the number of tickets.
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which ordered pair belongs on the ticket graph for 2 tickets?

    1. A(2, 90)
    2. B(2, 45)
    3. C(2, 47)
    4. D(90, 2)
    Steps to try
    1. Which quantity goes first in the ordered pair?
    2. Tickets is the independent variable, so it comes first.
    3. The second number is 2 × 45.
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    On the ticket graph, what should the two axes be labeled?

    1. ANumber of tickets and price of one ticket
    2. BNumber of tickets and total cost
    3. CTotal cost and $45
    4. DNumber of games and number of tickets
    Steps to try
    1. Which TWO quantities change in this situation?
    2. One is the choice; the other responds to it.
    3. You choose the tickets, and the total cost responds.
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    The Sandia Peak tram travels 1,200 feet each minute. How far has it traveled after 3 minutes?

    1. A1,200 feet
    2. B1,203 feet
    3. C2,400 feet
    4. D3,600 feet
    Steps to try
    1. How far does the tram go in ONE minute?
    2. Each minute adds another 1,200 feet.
    3. Multiply 1,200 by the number of minutes.
    Show your work

Explain your thinkingFind a card you called a match and your partner did not. Pick one ordered pair from it and test it in cost = 45 × tickets — what does the point on the graph tell you that the table does not?

Sentence starter The ordered pair ___ does / does not match because 45 × ___ = ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help