Examples of proportional and non-proportional tables with solutions

📚 Quick Study Guide

• ⚖️ Proportional Relationship: A relationship between two variables where their ratio is constant. This can be represented by the equation $y = kx$, where $k$ is the constant of proportionality.
• 📈 Identifying Proportional Tables: Look for a constant ratio between $y$ and $x$ values. Divide each $y$ value by its corresponding $x$ value. If the result is the same for all pairs, the table represents a proportional relationship.
• 🧮 Constant of Proportionality (k): This is the constant value that relates $x$ and $y$ in a proportional relationship. It's calculated as $k = \frac{y}{x}$.
• 🚫 Non-Proportional Relationship: A relationship where the ratio between two variables is NOT constant. The equation cannot be written in the form $y = kx$.
• ✍️ Identifying Non-Proportional Tables: The ratio between $y$ and $x$ values will vary. There is no constant value when you divide each $y$ value by its corresponding $x$ value.
• ➕ Additive Relationships: Non-proportional relationships are often additive. For example, $y = x + b$, where $b$ is a constant that's not zero.

Practice Quiz

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

   1. x	y
      1	2
      2	5
      3	8

   2. x	y
      1	3
      2	6
      3	9

   3. x	y
      1	4
      2	7
      3	10

   4. x	y
      1	5
      2	9
      3	13

2. What is the constant of proportionality in the table where x = 4, y = 12; x = 6, y = 18; x = 8, y = 24?
   1. 2
   2. 3
   3. 4
   4. 5
3. Which equation represents a non-proportional relationship?
   1. $y = 5x$
   2. $y = \frac{1}{2}x$
   3. $y = x + 3$
   4. $y = 0.75x$
4. In a proportional table, if x doubles, what happens to y?
   1. y halves
   2. y remains the same
   3. y doubles
   4. y triples
5. Which table does NOT represent a proportional relationship?

   1. x	y
      2	4
      4	8
      6	12

   2. x	y
      1	5
      3	15
      5	25

   3. x	y
      1	2
      2	3
      3	4

   4. x	y
      3	6
      5	10
      7	14

6. If $y = kx$ and when $x = 5$, $y = 20$, what is the value of k?
   1. 2
   2. 3
   3. 4
   4. 5
7. Which of the following situations represents a proportional relationship?
   1. The cost of renting a car is \$20 per day plus a \$30 insurance fee.
   2. The height of a plant increases by 2 inches each week.
   3. The number of students increases linearly over the years.
   4. The distance traveled by a car moving at a constant speed.