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Standard Form of a Line

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.

Standard form writes a line as Ax + By = C. It is useful for finding x- and y-intercepts because one variable becomes zero at each intercept. In Functions, Linear Relationships, and Rate of Change, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.

What you'll learn

Why it matters: Standard form is useful when two resources trade off, such as time and money, two ingredients in a mix, or two products sharing a budget.

Worked example

Problem. Find the intercepts of 2x + 3y = 12.

  1. Set y = 0: 2x = 12, so x = 6.
  2. Set x = 0: 3y = 12, so y = 4.
  3. The intercepts are (6, 0) and (0, 4).
  4. Connect the result back to Standard Form of a Line so the method and meaning are both clear.

Answer: x-intercept 6, y-intercept 4

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 equation is in standard form?

Choices: 3x + 2y = 12 · y = 3x + 2 · y - 4 = 2(x + 1) · x = 5

Show solution
  1. Standard form looks like Ax + By = C.

Answer: 3x + 2y = 12

2. For x + y = 9, what is the x-intercept?

Show solution
  1. Set y = 0.
  2. x = 9.

Answer: 9

3. For x + y = 9, what is the y-intercept?

Show solution
  1. Set x = 0.
  2. y = 9.

Answer: 9

4. For 4x + 2y = 20, what is the x-intercept?

Show solution
  1. Set y = 0.
  2. 4x = 20, so x = 5.

Answer: 5

5. For 4x + 2y = 20, what is the y-intercept?

Show solution
  1. Set x = 0.
  2. 2y = 20, so y = 10.

Answer: 10

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