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Parallel and Perpendicular Lines

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.

Parallel lines have the same slope and different intercepts. Perpendicular lines meet at right angles, so their slopes are opposite reciprocals. 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: Designers, builders, mapmakers, and robotics teams use parallel and perpendicular lines to keep paths, walls, rails, and supports aligned.

Worked example

Problem. Find the slope of a line perpendicular to y = 2x + 5.

  1. The given slope is 2.
  2. A perpendicular slope is the opposite reciprocal.
  3. The opposite reciprocal of 2 is -1/2.
  4. Connect the result back to Parallel and Perpendicular Lines so the method and meaning are both clear.

Answer: -1/2

Practice problems

1. What slope is parallel to y = 3x - 8?

Show solution
  1. Warm-up: First identify exactly what the question is asking: What slope is parallel to y = 3x - 8?
  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. Parallel lines have the same slope.
  4. Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: 3

2. What slope is parallel to y = -5x + 1?

Show solution
  1. Warm-up: First identify exactly what the question is asking: What slope is parallel to y = -5x + 1?
  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. Use the same slope for a parallel line.
  4. Check the result by substituting or estimating: the response should match -5 and make sense in the original problem.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: -5

3. Lines with slopes 4 and 4 are...

Choices: Parallel · Perpendicular · Neither · The same point

Show solution
  1. Warm-up: First identify exactly what the question is asking: Lines with slopes 4 and 4 are...
  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. Equal slopes are parallel unless they are the exact same line.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: Parallel

4. What slope is perpendicular to a line with slope 2?

Show solution
  1. Core Practice: First identify exactly what the question is asking: What slope is perpendicular to a line with slope 2?
  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. Flip 2 to 1/2 and change the sign.
  4. Check the result by substituting or estimating: the response should match -1/2 and make sense in the original problem.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: -1/2

5. What slope is perpendicular to a line with slope -3?

Show solution
  1. Core Practice: First identify exactly what the question is asking: What slope is perpendicular to a line with slope -3?
  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. Flip 3 to 1/3 and change the sign to positive.
  4. Check the result by substituting or estimating: the response should match 1/3 and make sense in the original problem.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: 1/3

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