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
- Compare slopes of parallel lines
- Find opposite reciprocal slopes
- Write equations for related lines
Worked example
Problem. Find the slope of a line perpendicular to y = 2x + 5.
- The given slope is 2.
- A perpendicular slope is the opposite reciprocal.
- The opposite reciprocal of 2 is -1/2.
- Connect the result back to Parallel and Perpendicular Lines so the method and meaning are both clear.
Answer: -1/2
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. What slope is parallel to y = 3x - 8?
Show solution
- Parallel lines have the same slope.
Answer: 3
2. What slope is parallel to y = -5x + 1?
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- Use the same slope for a parallel line.
Answer: -5
3. Lines with slopes 4 and 4 are...
Choices: Parallel · Perpendicular · Neither · The same point
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- Equal slopes are parallel unless they are the exact same line.
Answer: Parallel
4. What slope is perpendicular to a line with slope 2?
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- Flip 2 to 1/2 and change the sign.
Answer: -1/2
5. What slope is perpendicular to a line with slope -3?
Show solution
- Flip 3 to 1/3 and change the sign to positive.
Answer: 1/3
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