Analyze Graphs of Relationships Between Two Variables

Read and interpret tables and graphs showing how two quantities change in relationship to one another.

6.EE.C.9 · Two-Variable Relationships
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
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Warm-Up

2 questions
Warm-Up 1
Look at the table below. What is y when x = 5?
x 1 2 3 4 5
y 3 6 9 12 ?
Vocabulary: A table organizes data in rows and columns. A pattern is a rule that repeats. Look at how y changes each time x increases by 1.
✓Correct! The pattern is y = 3x. Each time x goes up by 1, y goes up by 3. So when x = 5, y = 15.
✗Not quite. Look at the pattern: 3, 6, 9, 12 ... y increases by 3 each time. So the next value is 12 + 3 = 15 (answer C).
Warm-Up 2
True or false: "A graph that goes up from left to right shows that as x increases, y decreases."
Vocabulary: A graph shows the relationship between two variables visually. If a line goes up from left to right, the y-values are getting larger, not smaller.
✓Correct! A graph going up from left to right means y increases as x increases, not decreases.
✗Think again: when a graph goes up from left to right, y is getting larger. The statement says y decreases, so it is false.
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Practice

5 questions
Practice 1
Complete the table using the rule y = 2x + 1.
How to use the rule: Replace x with the number in the top row, then multiply by 2 and add 1.
Example: When x = 1, y = 2(1) + 1 = 3.
x = 1: y =
x = 2: y =
x = 3: y =
x = 4: y =
x = 5: y =

Sentence frame: "I found each y-value by substituting x into the rule y = 2x + 1. When x = ___, y = 2(___) + 1 = ___."

✓All correct! The y-values are 3, 5, 7, 9, 11. Notice y increases by 2 each time x increases by 1.
✗Some values need another look. Remember: multiply x by 2, then add 1. The correct values are 3, 5, 7, 9, 11.
Practice 2
Which description best matches the graph below?
1 2 3 4 0 2 4 6 8 Number of Items Total Cost ($)
Reading a graph: Look at the coordinate pairs (x, y) on the graph. As x moves right, does y go up or down? By how much each time?
Explain your reasoning:

Sentence frame: "The graph shows that as x increases by 1, y increases by ___. This means each item costs $___."

✓Correct! The graph shows the points (1,2), (2,4), (3,6), (4,8). Each item adds $2 to the total cost.
✗Look at the y-values: 2, 4, 6, 8. Each goes up by 2. The answer is B: the total cost increases by $2 each time.
Practice 3
Match each table to the description that fits its pattern.
Vocabulary: A relationship describes how two variables change together. Look at how y changes as x increases by 1. Does y go up by the same amount? Does it double?
x: 1,2,3,4 → y: 3,6,9,12
x: 1,2,3,4 → y: 2,4,8,16
x: 1,2,3,4 → y: 5,5,5,5
x: 1,2,3,4 → y: 10,8,6,4
y increases by 3 each time
y doubles each time
y stays the same
y decreases by 2 each time
✓All correct! You identified all four patterns: +3, doubling, constant, and −2.
✗Some matches are wrong. Look at the differences between consecutive y-values in each table and try again.
Practice 4
A student tracked hours spent studying and test scores. What is the pattern in the table?
Hours Studying 1 2 3 4 5
Test Score 65 70 75 80 85
Hint: Look at the pattern in the test scores. What happens to the score each time the student studies one more hour? Subtract consecutive scores: 70 − 65 = ?
Explain the pattern you found:

Sentence frame: "Each time the student studies ___ more hour(s), the test score goes up by ___. This means the pattern is ___."

✓Correct! The test score increases by 5 points for each additional hour of studying: 65, 70, 75, 80, 85.
✗Find the difference: 70 − 65 = 5, 75 − 70 = 5, and so on. The score goes up by 5 each hour (answer B).
Practice 5
True or false: "If a graph is a straight line that passes through the origin (0, 0), the relationship is proportional."
Vocabulary: A proportional relationship means y = kx for some constant k. Its graph is always a straight line through the origin (the point where x = 0 and y = 0).
Explain your reasoning:
✓Correct! A proportional relationship has a constant rate (y = kx) and its graph is always a straight line through (0, 0).
✗Actually, this is true. A straight line through the origin means y is always a constant multiple of x, which is the definition of a proportional relationship.
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Challenge

1 question
Challenge
The graph below shows a car's journey over time. Describe what is happening during each section of the trip. What does each part of the graph tell you about the car's speed?
0 1 2 3 4 5 6 0 30 60 90 120 Time (hours) Distance (miles) A B C
Reading guide: This graph shows distance on the y-axis and time on the x-axis. A steep line means moving fast. A flat line means stopped (no distance gained). A gentle slope means moving slowly.
Section A (blue) = hours 0–2
Section B (gold) = hours 2–4
Section C (teal) = hours 4–6
Section A (hours 0–2):
Section B (hours 2–4):
Section C (hours 4–6):

Sentence frame: "In section ___, the car traveled ___ miles in ___ hours. The line is ___ (steep/flat/gentle), which means the car was ___ (moving fast/stopped/moving slowly)."

✓Great response! Section A: the car traveled 60 miles in 2 hours (moving fast, 30 mph). Section B: the car stopped for 2 hours (distance stayed at 60 miles). Section C: the car traveled 30 more miles in 2 hours (moving slowly, 15 mph).
✗Try to describe each section more fully. Look at whether the line is going up (moving), flat (stopped), steep (fast), or gentle (slow).