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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).
  4. Connect the result back to Graphing Lines from Tables and Equations so the method and meaning are both clear.

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

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

Practice problems

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

Show solution
  1. Substitute 0 for x.
  2. 2(0) + 3 = 3.

Answer: 3

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

Show solution
  1. Substitute 6.
  2. 6 - 4 = 2.

Answer: 2

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

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

Show solution
  1. When x = 2, y = 3(2) + 1 = 7.

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. Each y-value increases by 3.
  2. The slope is 3.

Answer: 3

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

Show solution
  1. Substitute x = 4.
  2. -2(4) + 5 = -3.

Answer: -3

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