Lesson 3.4Determine Equivalent Ratios Using 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.
Why This Matters The organizers of a soccer league ordered 6 of the bags shown to hold soccer balls. Each bag holds the same number of soccer balls. How many soccer balls will the bags hold?
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. | x across, y up |
| Ordered pairSpanish: Par ordenado | Two numbers (x, y) that tell where a point is on a grid. | (2, 14) |
| 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 pages, 0 stickers |
| 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 example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Each tray holds 8 muffins (x = trays, y = muffins). Write and plot three points.
- Table: 1 tray = 8, 2 trays = 16, 3 trays = 24.
- Pairs: (1, 8), (2, 16), (3, 24).
- Plot each pair from (0, 0): across x, then up y.
Answer: The points lie on one straight line through (0, 0)
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A recipe uses 1 cup of sugar for every 3 cups of flour.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The point ( , ) means .
- The origin means .
- I found y by multiplying x by .
- The points form a straight line because .
Word bank coordinate planeordered pairoriginx-axisy-axisplotpointstraight linetablemultiplyacrossup
Watch out!A common mistake
A common mistake in Graph Ratio Tables is writing the ordered pair in the wrong order
Lesson 3.4Determine Equivalent Ratios Using Graphs
Level 0Most support · every hint printed
Learning target I can graph the values from a ratio table as points on the coordinate plane.
Why This Matters The organizers of a soccer league ordered 6 of the bags shown to hold soccer balls. Each bag holds the same number of soccer balls. How many soccer balls will the bags hold?
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Each tray holds 8 muffins (x = trays, y = muffins). Write and plot three points.
- Table: 1 tray = 8, 2 trays = 16, 3 trays = 24.
- Pairs: (1, 8), (2, 16), (3, 24).
- Plot each pair from (0, 0): across x, then up y.
Answer: The points lie on one straight line through (0, 0)
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1Circle the letter of the best answer. Show how you know.
A ratio table shows (2, 6), (4, 12), and (6, 18). Which ordered pair comes next if the pattern continues?
- A(7, 20)
- B(8, 24)
- C(8, 22)
- D(10, 24)
Steps to try- Watch each coordinate separately: x goes 2, 4, 6, … and y goes 6, 12, 18, …
- Find the jump in the x-values and the jump in the y-values, then apply both jumps to (6, 18).
- The x-values climb by 2, so add 2 to the 6 first. Then find the y-jump from 6 → 12 → 18 and add it to 18.
Show your work -
2Circle the letter of the best answer. Show how you know.
When you graph equivalent ratios, the points will always form what shape?
- AA curved line
- BA straight line through the origin
- CA zigzag
- DA circle
Steps to try- Think about what happened when you plotted equivalent-ratio points earlier in this lesson.
- Equivalent ratios grow steadily: every time x rises by the same amount, y rises by the same amount. What shape is steady growth?
- Picture plotting (1, 2), (2, 4), (3, 6) and connecting them — and check whether (0, 0) would fit the pattern too.
Show your work -
3Circle the letter of the best answer. Show how you know.
A ratio table shows (2, 8), (3, 12), and (5, 20). What is the y-value when x = 7?
- A21
- B24
- C28
- D35
Steps to try- Compare each pair: 2 → 8, 3 → 12, 5 → 20. What is done to x to get y every time?
- Find the multiplier by dividing y by x for any pair — it should be the same for all three. Then apply it to x = 7.
- Divide 8 ÷ 2 to find the rule's multiplier. Then multiply 7 by that number.
My work — one step per line What I did to both sides - 1LookWhat is done to the variable?
- 2UndoDo the opposite — both sides.
- 3SimplifyOne side at a time.
- 4CheckPut it back in.
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4Circle the letter of the best answer. Show how you know.
Which point would NOT be on the graph of the ratio 1:5?
- A(2, 10)
- B(3, 10)
- C(4, 20)
- D(5, 25)
Steps to try- On the 1:5 graph, every y-value is exactly 5 times its x-value.
- Test each point: multiply its x by 5 and see whether you land on its y. You're hunting for the one that misses.
- Work through the points in order, multiplying each x by 5. The one whose y does not match is the answer.
Show your work
Explain your thinkingWhat pattern do the plotted points make? How does the graph show the ratio of 1 sundae to 2 ounces of sauce?
Sentence starter Every time the sundaes go up by ___, the ounces go up by ___, so the points line up in a ___ starting from ___.