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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.

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).

Answer: (5, 10)

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. Warm-up: First identify exactly what the question is asking: Which ordered pair comes from x = 3 and y = 8?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Ordered pairs are written (x, y).
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: (3, 8)

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: For y = 5x, what is y when x = 4?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute x = 4.
  4. 5 x 4 = 20.
  5. Check the result by substituting or estimating: the response should match 20 and make sense in the original problem.

Answer: 20

3. Which point must be on every proportional graph?

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which point must be on every proportional graph?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. A proportional relationship has the form y = kx.
  4. When x = 0, y = 0.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

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. Core Practice: First identify exactly what the question is asking: A table has x: 1, 2, 3 and y: 4, 8, 12. What is the constant of proportionality?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Divide y by x for any row.
  4. 4 divided by 1 is 4, and 8 divided by 2 is 4.
  5. Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.

Answer: 4

5. Which point fits y = 3x?

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

Show solution
  1. Core Practice: First identify exactly what the question is asking: Which point fits y = 3x?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. If x = 4, then y = 3 x 4 = 12.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: (4, 12)

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