CMClearMathAcademy

Graphing Lines from Tables and Equations

A free Algebra I lesson from the “Functions, Linear Relationships, and Rate of Change” unit, with a worked example and practice problems including step-by-step solutions.

A linear table has a constant rate of change: each time the input changes by the same amount, the output changes by the same amount. This constant change is the slope. Tables matter because they show patterns before an equation or graph is written. To work with a table, compare consecutive x-values and y-values, divide the change in y by the change in x, and then use that rate to extend the pattern or build an equation. A common mistake is noticing that outputs increase without checking whether the increase is constant.

What you'll learn

Why it matters: Tables help compare sales, distances, scores, temperatures, and experiment data before writing equations or graphing trends.

Worked example

Problem. Make two points for y = 2x + 1 using x = 0 and x = 3.

  1. Substitute x = 0: y = 2(0) + 1 = 1.
  2. Substitute x = 3: y = 2(3) + 1 = 7.
  3. The points are (0, 1) and (3, 7).

Answer: (0, 1) and (3, 7)

Practice problems

1. For y = 2x + 3, what is y when x = 0?

Show solution
  1. Warm-up: First identify exactly what the question is asking: For y = 2x + 3, what is y when x = 0?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute 0 for x.
  4. 2(0) + 3 = 3.
  5. Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.

Answer: 3

2. For y = x - 4, what is y when x = 6?

Show solution
  1. Warm-up: First identify exactly what the question is asking: For y = x - 4, what is y when x = 6?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute 6.
  4. 6 - 4 = 2.
  5. Check the result by substituting or estimating: the response should match 2 and make sense in the original problem.

Answer: 2

3. Which point is on y = 3x + 1?

Choices: (2, 7) · (2, 5) · (1, 3) · (0, 3)

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which point is on y = 3x + 1?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. When x = 2, y = 3(2) + 1 = 7.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: (2, 7)

4. A table has y-values 4, 7, 10, 13 as x increases by 1. What is the slope?

Show solution
  1. Core Practice: First identify exactly what the question is asking: A table has y-values 4, 7, 10, 13 as x increases by 1. What is the slope?
  2. For slope or rate of change, compare vertical change to horizontal change and keep the sign attached to the direction of the change.
  3. Each y-value increases by 3.
  4. The slope is 3.
  5. Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.

Answer: 3

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

Show solution
  1. Core Practice: First identify exactly what the question is asking: For y = -2x + 5, what is y when x = 4?
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Substitute x = 4.
  4. -2(4) + 5 = -3.
  5. Check the result by substituting or estimating: the response should match -3 and make sense in the original problem.

Answer: -3

Practice this interactively with instant feedback and an AI tutor.

Practice Graphing Lines from Tables and Equations Take the free placement check

More Algebra I lessons