Read the equations in the table below. Then drag a description of the situation and a table to represent each equation. Indicate whether each of the relationships is proportional or non-proportional.
proportional
Justin gets 3
cookies for every $1
he spends at the bakery.
non-proportional
2-column table. First column, x, with entries, 0, 1, 2, 3, 4. Second column, y, with entries, 3, 4, 5, 6, 7.
2-column table. First column, x, with entries, 0, 1, 2, 3, 4. Second column, y, with entries, 0, 3, 6, 9, 12.
Justin buys 3
more cookies than donuts at the bakery.
Situation
Table
Equation
Type of Relationship
y=3x
y=x+3
Situation: Justin's cookie purchases in relation to his spending at the bakery.
Table:
| x (dollars spent) | y (number of cookies) |
|------------------|----------------------|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
Equation: y = 3x
Type of Relationship: Proportional
Situation: Justin's cookie purchases in relation to his donut purchases at the bakery.
Table:
| x (number of donuts) | y (number of cookies) |
|----------------------|----------------------|
| 0 | 0 |
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
Equation: y = 3x
Type of Relationship: Proportional
Situation: Justin's cookie purchases compared to his donut purchases at the bakery.
Table:
| x (number of donuts) | y (number of cookies) |
|----------------------|----------------------|
| 0 | 3 |
| 1 | 4 |
| 2 | 5 |
| 3 | 6 |
| 4 | 7 |
Equation: y = x + 3
Type of Relationship: Non-Proportional
Situation: Justin gets 3 cookies for every $1 he spends at the bakery.
Table:
| x (Amount spent in dollars) | y (Number of cookies) |
|----------------------------|-----------------------|
| 0 | 0 |
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
Equation: y = 3x
Type of Relationship: Proportional
Explanation: As Justin spends more money at the bakery (x increases), he gets more cookies (y increases). The relationship between the amount spent and the number of cookies is proportional since it can be represented by a linear equation y = 3x.
Situation: Justin buys 3 more cookies than donuts at the bakery.
Table:
| x (Number of donuts) | y (Number of cookies) |
|----------------------|-----------------------|
| 0 | 3 |
| 1 | 4 |
| 2 | 5 |
| 3 | 6 |
| 4 | 7 |
Equation: y = x + 3
Type of Relationship: Non-proportional
Explanation: The number of cookies (y) is not directly proportional to the number of donuts (x). Even though the number of donuts increases by 1, the number of cookies only increases by 1. Therefore, the relationship is non-proportional. The equation that represents this relationship is y = x + 3.