Solved Examples: Parallel and Perpendicular Line Equations

📚 Quick Study Guide

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• Parallel Lines: Have the same slope ($m_1 = m_2$).
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• Perpendicular Lines: Slopes are negative reciprocals of each other ($m_1 = -\frac{1}{m_2}$ or $m_1 * m_2 = -1$).
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• Slope-Intercept Form: A linear equation is often expressed as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
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• Point-Slope Form: The equation of a line given a point $(x_1, y_1)$ and slope $m$ is $y - y_1 = m(x - x_1)$.
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• 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 $y = 4x - 2$