Interactive Quiz: Graphing Proportional Relationships from Tables

📚 Quick Study Guide

• 📊 Definition: A proportional relationship between two variables, $x$ and $y$, can be represented by the equation $y = kx$, where $k$ is the constant of proportionality.
• 📈 Identifying from Tables: Check if the ratio $\frac{y}{x}$ is constant for all pairs of $x$ and $y$ in the table. If it is, the relationship is proportional.
• 🧭 Finding the Constant of Proportionality (k): To find $k$, divide any $y$ value by its corresponding $x$ value ($k = \frac{y}{x}$).
• 💡 Graphing Proportional Relationships: The graph of a proportional relationship is a straight line that passes through the origin (0,0).
• 📝 Key Characteristics: The relationship must be linear and pass through the origin to be considered proportional.

Practice Quiz

1. Which of the following tables represents a proportional relationship?

   1. x	y
      1	2
      2	4
      3	6

   2. x	y
      1	3
      2	5
      3	7

   3. x	y
      1	1
      2	4
      3	9

   4. x	y
      0	1
      1	2
      2	3

2. What is the constant of proportionality ($k$) for the following table?

   x	y
   2	8
   4	16
   6	24

   1. 2
   2. 4
   3. 6
   4. 8
3. Which equation represents the proportional relationship in the table below?

   x	y
   1	5
   2	10
   3	15

   1. $y = x + 4$
   2. $y = 5x$
   3. $y = x - 5$
   4. $y = \frac{x}{5}$
4. A table shows the relationship between hours worked ($x$) and money earned ($y$). If the constant of proportionality is 12, what does this mean?
   1. For every hour worked, $1 is earned.
   2. For every hour worked, $12 is earned.
   3. For every $1 earned, 12 hours are worked.
   4. The person earns $12 regardless of how many hours they work.
5. Which table does NOT represent a proportional relationship?

   1. x	y
      2	6
      4	12
      6	18

   2. x	y
      1	4
      3	12
      5	20

   3. x	y
      2	5
      4	10
      6	15

   4. x	y
      0	0
      2	8
      5	20

6. In a proportional relationship, if $y = 24$ when $x = 6$, what is the value of $y$ when $x = 3$?
   1. 6
   2. 8
   3. 10
   4. 12
7. Which of the following graphs represents a proportional relationship?
   1. A straight line that does not pass through the origin.
   2. A curved line that passes through the origin.
   3. A straight line that passes through the origin.
   4. A curved line that does not pass through the origin.