Test questions on understanding and applying parallel line slope relationships.

📚 Quick Study Guide

• 📐 Parallel Lines: Two lines are parallel if and only if they have the same slope.
• 📈 Slope-Intercept Form: A line can be represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• ➕ Equal Slopes: If line 1 has a slope of $m_1$ and line 2 has a slope of $m_2$, then for the lines to be parallel, $m_1 = m_2$.
• ✍️ Finding the Equation: Given a point $(x_1, y_1)$ and a slope $m$, the point-slope form of a line is $y - y_1 = m(x - x_1)$.
• 🧭 Horizontal Lines: Horizontal lines have a slope of 0 and their equation is of the form $y = c$, where $c$ is a constant.
• 🧱 Vertical Lines: Vertical lines have an undefined slope and their equation is of the form $x = c$, where $c$ is a constant. Parallel vertical lines will have different $c$ values.

Practice Quiz

1. What is the slope of a line parallel to $y = 3x + 5$?
   1. 3
   2. -3
   3. 1/3
   4. -1/3
2. Which of the following lines is parallel to $y = -2x + 1$?
   1. $y = 2x - 1$
   2. $y = -2x + 3$
   3. $y = \frac{1}{2}x + 1$
   4. $y = -\frac{1}{2}x - 2$
3. 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. $y = 4x - 6$
4. Which line is parallel to the x-axis?
   1. $x = 5$
   2. $y = x$
   3. $y = -3$
   4. $x = y$
5. If a line has a slope of $\frac{2}{3}$, what is the slope of any line parallel to it?
   1. $-\frac{2}{3}$
   2. $\frac{3}{2}$
   3. $-\frac{3}{2}$
   4. $\frac{2}{3}$
6. Which of the following equations represents a line parallel to $x = 4$?
   1. $y = 4$
   2. $x = -4$
   3. $y = -4$
   4. $x = 0$
7. What must be true about the slopes ($m_1$ and $m_2$) of two parallel lines?
   1. $m_1 = -m_2$
   2. $m_1 = \frac{1}{m_2}$
   3. $m_1 = m_2$
   4. $m_1 * m_2 = -1$