Question
Graphs proportional relationships, Quick check math 7A, 6.24 unit rates and proportions
Answers
GPT-4o mini
I don't have access to specific content from textbooks or other proprietary materials, including "Quick Check Math 7A." However, I can explain the concepts related to proportional relationships, unit rates, and how to graph these relationships.
### Proportional Relationships
A proportional relationship is a relationship between two quantities where their ratio is constant. For instance, if we have two variables, \(x\) and \(y\), they are in a proportional relationship if:
\[ \frac{y_1}{x_1} = \frac{y_2}{x_2} = k \]
where \(k\) is a constant.
### Unit Rates
A **unit rate** is a comparison of two different quantities when they are combined together. It expresses one quantity in relation to one unit of another. For example, if you travel 60 miles in 2 hours, the unit rate is:
\[ \text{Unit Rate} = \frac{60 \text{ miles}}{2 \text{ hours}} = 30 \text{ miles per hour} \]
### Graphing Proportional Relationships
To graph a proportional relationship:
1. **Table of Values**: Create a table of values where \(x\) and \(y\) are in a proportional relationship. For example, if \(y = 2x\), you might have:
| \(x\) | \(y\) |
|-------|-------|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
2. **Plot Points**: Plot the points from the table on a coordinate grid.
3. **Draw a Line**: Since it's a proportional relationship, the points will all lie on a straight line that passes through the origin (0, 0).
### Example
If you want to graph the relationship where \(y = 3x\):
1. **Make a Table**:
| \(x\) | \(y\) |
|-------|-------|
| 0 | 0 |
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
2. **Plot the points** (0, 0), (1, 3), (2, 6), (3, 9) on a graph.
3. **Draw a Line**: Connect the points with a straight line through the origin.
If you have any specific questions or problems related to these topics, feel free to ask!
### Proportional Relationships
A proportional relationship is a relationship between two quantities where their ratio is constant. For instance, if we have two variables, \(x\) and \(y\), they are in a proportional relationship if:
\[ \frac{y_1}{x_1} = \frac{y_2}{x_2} = k \]
where \(k\) is a constant.
### Unit Rates
A **unit rate** is a comparison of two different quantities when they are combined together. It expresses one quantity in relation to one unit of another. For example, if you travel 60 miles in 2 hours, the unit rate is:
\[ \text{Unit Rate} = \frac{60 \text{ miles}}{2 \text{ hours}} = 30 \text{ miles per hour} \]
### Graphing Proportional Relationships
To graph a proportional relationship:
1. **Table of Values**: Create a table of values where \(x\) and \(y\) are in a proportional relationship. For example, if \(y = 2x\), you might have:
| \(x\) | \(y\) |
|-------|-------|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
2. **Plot Points**: Plot the points from the table on a coordinate grid.
3. **Draw a Line**: Since it's a proportional relationship, the points will all lie on a straight line that passes through the origin (0, 0).
### Example
If you want to graph the relationship where \(y = 3x\):
1. **Make a Table**:
| \(x\) | \(y\) |
|-------|-------|
| 0 | 0 |
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
2. **Plot the points** (0, 0), (1, 3), (2, 6), (3, 9) on a graph.
3. **Draw a Line**: Connect the points with a straight line through the origin.
If you have any specific questions or problems related to these topics, feel free to ask!