Lesson 3.4Interpreting Points on Ratio Graphs
Start hereWords, worked example, and sentence starters
Learning target I can graph the values from a ratio table as points on the coordinate plane.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Coordinate planeSpanish: Plano cartesiano | A grid with a line going across and a line going up to plot points. | A + shape made by two number lines crossing at the center point (0, 0) |
| Ordered pairSpanish: Par ordenado | Two numbers (x, y) that tell where a point is on a grid. | (3, 6) means go right 3, up 6 |
| Linear patternSpanish: Patrón lineal | Points that make a straight line on a grid. | (1,2), (2,4), (3,6) all line up |
| ProportionalSpanish: Proporcional | Two amounts that grow together at the same rate. | A straight line from (0,0) through (2,6) and (4,12) |
| OriginSpanish: Origen | The point (0, 0) where the two grid lines cross. | (0, 0) |
| Ratio tableSpanish: Tabla de razones | A table of equal ratios that shows a pattern. | Cups of juice: 2, 4, 6 | Cups of water: 3, 6, 9 |
How it worksWorked examplereading the meaning of a point
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A graph shows crayons in boxes (x = boxes, y = crayons). The line passes through (1, 9).
- Find the unit rate point (1, r). r = 9, so 1 box holds 9 crayons.
- Read x FIRST, then y — never flip them.
- Interpret another point. (4, 36) means 4 boxes hold 36 crayons.
- Predict with the unit rate. 7 boxes: 7 × 9 = 63 → (7, 63)
Answer: (1, 9) is the unit rate: 1 box holds 9 crayons.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A graph shows apples in bags (x = bags, y = apples). The line passes through (1, 6).
- Find the unit rate point ( 1 , r ). r = , so 1 bag holds apples.
- Interpret ( 4 , 24 ). bags hold apples.
- Is ( 7 , 42 ) on this line? 7 × = , so .
- The origin ( 0 , 0 ) means
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The point ( , ) means .
- The unit rate is because the point ( 1 , ) is on the line.
- The origin ( 0 , 0 ) means .
- I know the point is on the line because .
Word bank unit rateorigininterpretcoordinatesx-valuey-valuepointlinefor eachmeanspredictflip
Watch outA common mistake
A common mistake in Graph Ratio Tables is writing the ordered pair in the wrong order — putting the second table value first instead of matching (x, y) to the table's column order. For example, if a recipe table shows 2 cups of sugar for every 4 cups of flour, a student might plot (4, 2) instead of (2, 4), landing the point in a completely different spot on the grid. Before you plot, check: which quantity goes on the x-axis, and does your ordered pair start with that number?
Lesson 3.4Interpreting Points on Ratio Graphs
Apply Day · Version ASupported practice
Learning target I can graph the values from a ratio table as points on the coordinate plane.
-
1Complete each step, then write the final answer.
Each bike adds 2 wheels. Where is the point for 4 bikes? Each bike has 2 wheels. Bikes are x and wheels are y. What is the y-value of the point for 4 bikes?
Show your workHint Multiply the bikes by 2.
Final answer: -
2Complete each step, then write the final answer.
Each pack has 4 pencils. Packs are x and pencils are y. The point for 3 packs is (3, ?). What is the missing number?
Show your workHint The missing number is y. Multiply the packs by 4.
Final answer: -
3Complete each step, then write the final answer.
Each table seats 6 students. Tables are x and students are y. What is the y-value of the point for 4 tables?
Show your workHint Multiply the tables by 6.
Final answer:
Lesson 3.4Interpreting Points on Ratio Graphs
Apply Day · Version BCore practice
Learning target I can graph the values from a ratio table as points on the coordinate plane.
-
1Circle the letter of the best answer. Show how you know.
The line starts at (0, 0) and goes through (1, 4). A recipe uses 4 cups of flour for every 1 cup of sugar. Sugar is x and flour is y. Which point is NOT on the graph?
- A(3, 7)
- B(2, 8)
- C(3, 12)
- D(0, 0)
Show your work -
2Complete each step, then write the final answer.
The points (1, 6) and (2, 12) are on a graph of equivalent ratios. What is the y-value when x = 5?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Each pack has 3 juice boxes. Packs are x and juice boxes are y. What is the y-value of the point for 4 packs?
Show your workFinal answer:
Lesson 3.4Interpreting Points on Ratio Graphs
Apply Day · ChallengeExtension
Learning target I can graph the values from a ratio table as points on the coordinate plane.
-
1Circle the letter of the best answer. Show how you know.
A ratio table pairs 1 hour with 45 miles, 2 hours with 90 miles, and 3 hours with 135 miles. Which ordered pair belongs on the graph of this relationship?
- A(4, 180)
- B(4, 45)
- C(4, 140)
- D(180, 4)
Show your work -
2Complete each step, then write the final answer.
A graph of equivalent ratios goes through (0, 0) and (6, 4). Lee says the point with y = 10 is (12, 10), because he added 6 to both numbers. What is the correct x-value?
Show your workFinal answer: -
3Complete each step, then write the final answer.
The points (3, 6) and (5, 10) are on a graph of equivalent ratios. What is the y-value when x = 9?
Show your workFinal answer: