Geometry Test Questions: Understanding Slope Types

📚 Quick Study Guide

• 📈 Positive Slope: Rises from left to right. As $x$ increases, $y$ increases.
• 📉 Negative Slope: Falls from left to right. As $x$ increases, $y$ decreases.
• ↔️ Zero Slope: A horizontal line. The equation is of the form $y = c$, where $c$ is a constant. The slope is $0$.
• ↕️ Undefined Slope: A vertical line. The equation is of the form $x = c$, where $c$ is a constant. The slope is undefined.
• 📐 Slope Formula: Given two points $(x_1, y_1)$ and $(x_2, y_2)$, the slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• 💡 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 type of slope does the line $y = -3x + 5$ have?
   1. Positive
   2. Negative
   3. Zero
   4. Undefined
2. A line passes through the points (2, 4) and (5, 4). What type of slope does it have?
   1. Positive
   2. Negative
   3. Zero
   4. Undefined
3. Which of the following lines has an undefined slope?
   1. $y = 3$
   2. $x = -2$
   3. $y = x + 1$
   4. $y = -x$
4. A line has a positive slope. Which statement is true?
   1. As x increases, y decreases.
   2. As x decreases, y increases.
   3. The line is horizontal.
   4. The line is vertical.
5. What type of slope is represented by a vertical line?
   1. Positive
   2. Negative
   3. Zero
   4. Undefined
6. A line has the equation $y = 7$. What is its slope?
   1. Positive
   2. Negative
   3. Zero
   4. Undefined
7. Which of the following points could lie on a line with a negative slope, given that the line also passes through the point (0, 5)?
   1. (1, 6)
   2. (2, 7)
   3. (3, 2)
   4. (4, 5)