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Graphing Relationships from Tables

A free Pre-Algebra lesson from the “Proportional Reasoning” unit, with a worked example and practice problems including step-by-step solutions.

A table can become a graph by turning each row into an ordered pair. In a proportional relationship, the graph is a straight line through the origin because every output is a constant multiple of the input. In Proportional Reasoning, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

Why it matters: Cell phone data plans, savings over time, and sports stats are tracked as relationships between two quantities. A graph from a table is how a pattern becomes visible at a glance.

Worked example

Problem. A table follows y = 2x. What point matches x = 5?

  1. Use x = 5 in y = 2x.
  2. y = 2 x 5 = 10.
  3. The ordered pair is (5, 10).
  4. Connect the calculation back to Graphing Relationships from Tables so the method, not just the arithmetic, is clear.

Answer: (5, 10)

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.

Practice problems

1. Which ordered pair comes from x = 3 and y = 8?

Choices: (3, 8) · (8, 3) · (3, 3) · (8, 8)

Show solution
  1. Ordered pairs are written (x, y).

Answer: (3, 8)

2. For y = 5x, what is y when x = 4?

Show solution
  1. Substitute x = 4.
  2. 5 x 4 = 20.

Answer: 20

3. Which point must be on every proportional graph?

Choices: (0, 0) · (1, 0) · (0, 1) · (1, 1)

Show solution
  1. A proportional relationship has the form y = kx.
  2. When x = 0, y = 0.

Answer: (0, 0)

4. A table has x: 1, 2, 3 and y: 4, 8, 12. What is the constant of proportionality?

Show solution
  1. Divide y by x for any row.
  2. 4 divided by 1 is 4, and 8 divided by 2 is 4.

Answer: 4

5. Which point fits y = 3x?

Choices: (4, 12) · (4, 7) · (12, 4) · (3, 4)

Show solution
  1. If x = 4, then y = 3 x 4 = 12.

Answer: (4, 12)

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