Lesson 9.2Analyzing a Graph
Start hereWords, worked example, and sentence starters
Learning target I can use a table and a graph to determine and analyze the relationship between two variable quantities.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| graphSpanish: gráfica | A picture on a coordinate plane that shows how two quantities are related. | Points (1, 45), (2, 90), (3, 135) climbing left to right — cost by tickets. |
| 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, 135): 3 tickets cost $135 — the independent quantity comes first. |
| axisSpanish: eje | One of the two number lines that frame a graph. Each axis is labeled with a quantity from the problem. | Horizontal axis: months. Vertical axis: total cost. |
| coordinatesSpanish: coordenadas | The numbers in an ordered pair that tell how far to move along each axis to reach a point. | In (4, 105), 4 says how far across and 105 how far up. |
| Rate of changeSpanish: Tasa de cambio | How much y changes each time x goes up by one. | up $4 per hour |
How it worksWorked examplereading a relationship off a graph
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A taxi graph passes through (1, 15), (2, 30), and (3, 45). Describe it, then find the cost of a 12-mile ride.
- Each point is (miles, dollars). The first point says one mile costs $15.
- Rate of change: from (1, 15) to (2, 30) the cost climbs $15 for each extra mile.
- Unit rate: $15 per mile. Multiply any number of miles by that rate.
- A 12-mile ride: 12 × 15 → $180. The path keeps the same steepness.
Answer: The cost climbs $15 per mile, so a 12-mile ride costs $180.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A printing graph passes through (1, 13), (2, 26), and (3, 39). Describe it, then find y when x is 4.
- Each point is ( , ).
- Rate of change: y climbs each time x goes up by one.
- Unit rate: for one unit of x. Multiply any x by that rate.
- When x is 4: 4 × → .
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The point ( , ) means that .
- Each time x goes up by one, y goes up by .
- The unit rate on this graph is per .
- This graph is steeper than that one because .
Word bank rate of changeunit ratesteeperoriginordered paircoordinatesaxispointclimbsperpredictstraight
Watch outA common mistake
Reversing the coordinates of a point — writing (cost, tickets) instead of (tickets, cost). The independent variable always comes first in the ordered pair.
Lesson 9.2Analyzing a Graph
Apply Day · Version ASupported practice
Learning target I can use a table and a graph to determine and analyze the relationship between two variable quantities.
-
1Complete each step, then write the final answer.
Use the same scale factor on both rows. Each ticket costs $6. Write the point for 5 tickets: (5, ?). What is the missing number?
Show your workHint The ? is the cost of 5 tickets.
Final answer: -
2Complete each step, then write the final answer.
Use the same scale factor on both rows. A bike rents for $7 each hour. What is the point for 4 hours on the graph of (hours, total cost)? Give the total cost.
Show your workHint Hours go first. Multiply to find the total cost.
Final answer: -
3Complete each step, then write the final answer.
Use the same scale factor on both rows. A graph of (hours, miles) passes through (1, 60). What is the point for 3 hours? Give the miles.
Show your workHint The point (1, 60) means 60 miles in 1 hour.
Final answer:
Lesson 9.2Analyzing a Graph
Apply Day · Version BCore practice
Learning target I can use a table and a graph to determine and analyze the relationship between two variable quantities.
-
1Circle the letter of the best answer. Show how you know.
Read each column as (hours, dollars). Mia earns $15 each hour. What does the point (4, 60) mean on her graph of (hours, dollars)?
- AMia earns $60 for 4 hours.
- BMia earns $4 for 60 hours.
- CMia earns $60 each hour.
Show your work
-
2Complete each step, then write the final answer.
Go to 1 first, then scale up. A graph of (hours, dollars) passes through (4, 34). The pay is the same each hour. What is the point for 1 hour? Give the dollars.
Show your workFinal answer: -
3Complete each step, then write the final answer.
Use the same scale factor on both rows. Notebooks cost $4 each. The graph of (notebooks, total cost) passes through (7, ?). What is the missing number?
Show your workFinal answer:
Lesson 9.2Analyzing a Graph
Apply Day · ChallengeExtension
Learning target I can use a table and a graph to determine and analyze the relationship between two variable quantities.
-
1Circle the letter of the best answer. Show how you know.
A stadium shuttle carries fans from the parking lot. The table pairs the number of trips with the total fans carried: 2 trips with 96 fans, 5 trips with 240 fans, and 8 trips with 384 fans. On a graph with trips on the horizontal axis and fans on the vertical axis, which ordered pair belongs to 3 trips?
- A(3, 51)
- B(3, 144)
- C(3, 48)
- D(144, 3)
Show your work -
2Circle the letter of the best answer. Show how you know.
Scale the unit rate to test each column. A table shows (minutes, pages): (2, 6), (4, 12) and (5, 16). One row does not fit the same rate. Which row?
- A(5, 16)
- B(4, 12)
- C(2, 6)
Show your work -
3Complete each step, then write the final answer.
Go to 1 first, then scale up. A graph of (minutes, gallons) passes through (5, 35). The rate stays the same. What is the point for 12 minutes? Give the gallons.
Show your workFinal answer: