Lesson 9.2Analyze Graphs of Relationships Between Two Variables
Set B · Version ASecond form · supported practice
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?
RememberAnalyze Graphs of Relationships Between Two Variables
Representing Two-Variable Relationships with Tables & Graphs. Formula: Table (x, y) → Graph Point (x, y) A table shows a relationship with numbers. A graph shows the same relationship with points. Reading either one tells you how the dependent variable responds to the independent variable.
- Construct table: Put independent variable in column 1 (x) and dependent in column 2 (y).
- Identify the rate of change or rule connecting x to y.
- Plot the ordered pairs on the coordinate plane with x on horizontal axis and y on vertical
Words: graph (gráfica)table of values (tabla de valores)ordered pair (par ordenado)axis (eje)coordinates (coordenadas)
-
1Write the name of the correct group on each line.
Sort each ordered pair (tickets, cost): on the graph, or not?
- (1, 45)
- (2, 90)
- (4, 180)
- (3, 120)
- (2, 100)
- (5, 200)
Hint Test each pair: does the cost equal 45 × the tickets?
-
2Complete the table. Show how you found each value.
Tickets cost $45 each. Complete the table that feeds the graph.
Tickets (x) Thinking Total cost in dollars (y) 2 5 8 Hint The independent variable (tickets) goes in column 1; the dependent (cost) responds in the last column.
Show your work
-
3Circle the letter of the best answer. Show how you know.
Songs cost $2 each. Which is the independent variable?
- AThe number of songs bought
- BThe total cost
- CThe $2 price
- DThe music store
Show your work -
4Circle the letter of the best answer. Show how you know.
"The longer you run, the more calories you burn." Which is the dependent variable?
- AMinutes run
- BCalories burned
- CThe runner
- DThe distance
Show your work -
5Circle the letter of the best answer. Show how you know.
A plant grows taller each day. Which sentence is correct?
- AThe number of days depends on height
- BHeight depends on the number of days
- CNeither one depends on the other
- DBoth are independent variables
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 × ___ = ___.
Lesson 9.2Analyze Graphs of Relationships Between Two Variables
Set B · Version BSecond form · core practice
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?
-
1Circle the letter of the best answer. Show how you know.
On the football ticket graph, what does the point (3, 135) represent?
- A3 tickets cost a total of $135
- B3 tickets cost $135 each
- C135 tickets cost a total of $3
- DThe game lasts 135 minutes
Show your work
-
2Circle the letter of the best answer. Show how you know.
In any relationship between two quantities, the independent variable is the one that…
- Ayou choose or control
- Bis always larger
- Cresponds to the other
- Dis always graphed vertically
Show your work -
3Circle the letter of the best answer. Show how you know.
Nakai opened a savings account with an initial deposit, or principal, of $750. The account earns 3.5% simple interest each year — interest is the amount earned for the use of the principal. A graph shows the interest Nakai has earned over a period of years, with points rising steadily. On Nakai's graph, which variable is plotted on the independent axis (x-axis)?
- Ayears
- Binterest earned
- Cprincipal amount
- Daccount balance
Show your work -
4Circle the letter of the best answer. Show how you know.
Nakai opened a savings account with an initial deposit, or principal, of $750. The account earns 3.5% simple interest each year — interest is the amount earned for the use of the principal. A graph shows the interest Nakai has earned over a period of years, with points rising steadily. Why does the graph rise by the same amount every year instead of curving upward more steeply over time?
- ANakai earns compound interest, which grows faster each year
- BThe interest rate increases by 3.5% every year
- CNakai deposits an extra $26.25 into the account every year
- DNakai earns simple interest — the same $26.25 each year, calculated only on the original $750 principal
Show your work -
5Circle the letter of the best answer. Show how you know.
Nakai opened a savings account with an initial deposit, or principal, of $750. The account earns 3.5% simple interest each year — interest is the amount earned for the use of the principal. A graph shows the interest Nakai has earned over a period of years, with points rising steadily. A point on the graph is located at (4, x). Based on the interest rate, what value of x makes this point correct?
- A$78.75
- B$105
- C$131.25
- D$855
Work