Online quiz: Understanding the constant of proportionality (Grade 7).

📚 Quick Study Guide

• 🔢 Constant of Proportionality: The constant value ($k$) that relates two proportional quantities, $x$ and $y$. It’s the ratio $\frac{y}{x}$.
• ⚖️ Proportional Relationship: A relationship between two variables where their ratio is constant. If $y$ is proportional to $x$, then $y = kx$, where $k$ is the constant of proportionality.
• 📝 Finding the Constant: To find $k$, divide any $y$ value by its corresponding $x$ value (i.e., $k = \frac{y}{x}$).
• 📈 Graphing Proportional Relationships: The graph of a proportional relationship is a straight line that passes through the origin (0, 0).
• 💡 Identifying Proportionality: Look for a constant ratio between the two quantities. If the ratio is always the same, they are proportional.

🧪 Practice Quiz

1. What is the constant of proportionality in the equation $y = 5x$?
   1. A) 1
   2. B) 5
   3. C) x
   4. D) y
2. If $y$ is proportional to $x$, and $y = 12$ when $x = 3$, what is the constant of proportionality?
   1. A) 36
   2. B) 4
   3. C) 9
   4. D) 15
3. Which equation represents a proportional relationship?
   1. A) $y = x + 2$
   2. B) $y = 3x$
   3. C) $y = x^2$
   4. D) $y = 2x + 1$
4. If the constant of proportionality is 7, and $x = 2$, what is the value of $y$?
   1. A) 5
   2. B) 9
   3. C) 14
   4. D) 21
5. A recipe requires 2 cups of flour for every 1 cup of sugar. What is the constant of proportionality of flour to sugar?
   1. A) 0.5
   2. B) 1
   3. C) 2
   4. D) 3
6. Which of the following graphs represents a proportional relationship?
   1. A) A curve
   2. B) A straight line not through the origin
   3. C) A straight line through the origin
   4. D) A zig-zag line
7. If $y = kx$ and $y = 24$ when $x = 6$, find the value of $k$.
   1. A) 30
   2. B) 18
   3. C) 4
   4. D) 144