graphing linear equations quiz

📚 Quick Study Guide

• 📈 Slope-Intercept Form: A linear equation can be written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• 🧭 Slope: The slope ($m$) represents the rate of change of $y$ with respect to $x$. It can be calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$ given two points $(x_1, y_1)$ and $(x_2, y_2)$.
• 📍 Y-Intercept: The y-intercept ($b$) is the point where the line crosses the y-axis (when $x = 0$).
• ↔️ X-Intercept: The x-intercept is the point where the line crosses the x-axis (when $y = 0$). To find it, set $y = 0$ in the equation and solve for $x$.
• 📐 Point-Slope Form: Another form of a linear equation is $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line.
• ✍️ Standard Form: A linear equation can also be written in standard form as $Ax + By = C$, where A, B, and C are constants.
• ∥ Parallel Lines: Parallel lines have the same slope.
• ⟂ Perpendicular Lines: Perpendicular lines have slopes that are negative reciprocals of each other (i.e., $m_1 * m_2 = -1$).

🧪 Practice Quiz

1. What is the slope of the line $y = 3x - 2$?
1. A) -2
2. B) 2/3
3. C) 3
4. D) -3
2. What is the y-intercept of the line $y = -2x + 5$?
1. A) -2
2. B) 5
3. C) 2
4. D) -5
3. Which equation represents a line with a slope of 2 and passing through the point (1, 4)?
1. A) $y = 2x + 4$
2. B) $y = 2x + 2$
3. C) $y = x + 4$
4. D) $y = 2x + 1$
4. What is the equation of a line passing through points (0, 2) and (1, 5)?
1. A) $y = 2x + 3$
2. B) $y = 3x + 2$
3. C) $y = 5x + 2$
4. D) $y = 3x + 5$
5. What is the x-intercept of the line $y = 4x - 8$?
1. A) 2
2. B) -2
3. C) 4
4. D) -8
6. Which of the following lines is parallel to $y = -x + 3$?
1. A) $y = x + 3$
2. B) $y = -x - 1$
3. C) $y = 2x + 3$
4. D) $y = -2x + 3$
7. Which of the following lines is perpendicular to $y = 2x - 1$?
1. A) $y = 2x + 1$
2. B) $y = -2x - 1$
3. C) $y = -\frac{1}{2}x + 3$
4. D) $y = \frac{1}{2}x - 1$