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karen_manning 1d ago • 0 views

Solved Examples: Parallel and Perpendicular Line Equations

Hey there! 👋 Let's conquer parallel and perpendicular line equations! I've got a quick study guide and practice quiz for you. Good luck! 🍀
🧠 General Knowledge

1 Answers

✅ Best Answer

📚 Quick Study Guide

    📏
  • Parallel Lines: Have the same slope ($m_1 = m_2$).
  • Perpendicular Lines: Slopes are negative reciprocals of each other ($m_1 = -\frac{1}{m_2}$ or $m_1 * m_2 = -1$).
  • 📝
  • Slope-Intercept Form: A linear equation is often expressed as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
  • 📍
  • Point-Slope Form: The equation of a line given a point $(x_1, y_1)$ and slope $m$ is $y - y_1 = m(x - x_1)$.
  • 📐
  • Standard Form: A linear equation can also be expressed as $Ax + By = C$.

Practice Quiz

  1. What is the slope of a line parallel to $y = 3x + 5$?
    1. 3
    2. -3
    3. $\frac{1}{3}$
    4. $-\frac{1}{3}$

  2. What is the slope of a line perpendicular to $y = -2x + 1$?
    1. -2
    2. 2
    3. $\frac{1}{2}$
    4. $-\frac{1}{2}$

  3. Which of the following lines is parallel to $2x + y = 4$?
    1. $y = 2x - 1$
    2. $y = -2x + 3$
    3. $y = \frac{1}{2}x + 2$
    4. $y = -\frac{1}{2}x - 4$

  4. Which of the following lines is perpendicular to $x - 3y = 6$?
    1. $y = 3x + 1$
    2. $y = -3x - 2$
    3. $y = \frac{1}{3}x + 4$
    4. $y = -\frac{1}{3}x - 5$

  5. A line passes through the point (1, 2) and is parallel to $y = 4x - 3$. What is the equation of the line?
    1. $y = 4x - 2$
    2. $y = 4x + 2$
    3. $y = -4x + 6$
    4. $y = -4x - 6$

  6. A line passes through the point (-2, 3) and is perpendicular to $y = -\frac{1}{2}x + 5$. What is the equation of the line?
    1. $y = -2x - 1$
    2. $y = 2x + 7$
    3. $y = -\frac{1}{2}x + 2$
    4. $y = \frac{1}{2}x - 4$

  7. Which pair of equations represents parallel lines?
    1. $y = 2x + 3$ and $y = -2x + 3$
    2. $y = 3x - 1$ and $y = -\frac{1}{3}x - 1$
    3. $y = -x + 2$ and $y = x + 2$
    4. $y = 4x + 5$ and $y = 4x - 2$
Click to see Answers
  1. A
  2. C
  3. B
  4. A
  5. A
  6. B
  7. D

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