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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.

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).

Answer: x-intercept 6, y-intercept 4

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. Warm-up: First identify exactly what the question is asking: Which equation is in standard form?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Standard form looks like Ax + By = C.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: 3x + 2y = 12

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: For x + y = 9, what is the x-intercept?
  2. For intercepts, remember that an x-intercept has y = 0 and a y-intercept has x = 0.
  3. Set y = 0.
  4. x = 9.
  5. Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.

Answer: 9

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: For x + y = 9, what is the y-intercept?
  2. For intercepts, remember that an x-intercept has y = 0 and a y-intercept has x = 0.
  3. Set x = 0.
  4. y = 9.
  5. Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.

Answer: 9

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

Show solution
  1. Core Practice: First identify exactly what the question is asking: For 4x + 2y = 20, what is the x-intercept?
  2. For intercepts, remember that an x-intercept has y = 0 and a y-intercept has x = 0.
  3. Set y = 0.
  4. 4x = 20, so x = 5.
  5. Check the result by substituting or estimating: the response should match 5 and make sense in the original problem.

Answer: 5

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

Show solution
  1. Core Practice: First identify exactly what the question is asking: For 4x + 2y = 20, what is the y-intercept?
  2. For intercepts, remember that an x-intercept has y = 0 and a y-intercept has x = 0.
  3. Set x = 0.
  4. 2y = 20, so y = 10.
  5. Check the result by substituting or estimating: the response should match 10 and make sense in the original problem.

Answer: 10

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