Parallel Lines And Slopes - Varsity Tutors

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Parallel Lines and Slopes

Study Guide

Key Definition

Parallel lines are coplanar lines that do not intersect and have the same slope. If two lines are parallel, their slopes are equal: $m_1 = m_2$.

Important Notes

  • Parallel lines have the same slope: $m_1 = m_2$
  • The equation of a line parallel to another can be written using the point-slope form.
  • Use $y - y_1 = m(x - x_1)$ to find parallel line equations.
  • Ensure the slopes are equal for lines to be parallel.
  • Parallel lines never intersect.

Mathematical Notation

$\parallel$ means parallelRemember to use proper notation when solving problems

Why It Works

Parallel lines remain equidistant and never meet, which is why their slopes must be identical: $m_1 = m_2$.

Remember

To find a parallel line, use the same slope: $m$ and the point-slope form of the equation.

Quick Reference

Slope of Parallel Lines:$m_1 = m_2$

Understanding Parallel Lines and Slopes

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

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Beginner Explanation

Two lines are parallel if they have the same slope. For example, if one line has slope m, any line with slope m is parallel to it.Now showing Beginner level explanation.

Practice Problems

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1

Quick Quiz

Single Choice QuizBeginner

What is the slope of a line parallel to the line $y = 3x + 4$?

A$3$B$4$C$-3$D$0$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

Imagine you are designing a ramp parallel to an existing one with slope $\frac{1}{4}$. How would you ensure the ramp is parallel?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Determine the equation of a line parallel to $y = -2x + 5$ that passes through the point $(1, 2)$.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Find the equation of a line parallel to $2x - 3y = 6$ that passes through $(-1, -2)$.

A$2x - 3y = -4$B$2x - 3y = -12$C$3x - 2y = 6$D$3x - 2y = -6$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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