The Equation C = 1 3 S C = \frac{1}{3}s C = 3 1 ​ S Represents The Proportional Relationship Between The Number Of Bags Of Cement ( C C C ) And The Number Of Bags Of Sand ( S S S ).Which Statement Is True?A. The Proportional Relationship Is Graphed

Introduction

In the world of mathematics, proportional relationships are a fundamental concept that helps us understand the relationship between two variables. The equation $c = \frac{1}{3}s$ represents a proportional relationship between the number of bags of cement ($c$) and the number of bags of sand ($s$). In this article, we will delve into the world of proportional relationships and explore the statement that is true.

Understanding Proportional Relationships

A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other variable. In other words, if we multiply one variable by a constant, we get the other variable. The equation $c = \frac{1}{3}s$ represents a proportional relationship where the number of bags of cement ($c$) is equal to one-third of the number of bags of sand ($s$).

Graphing Proportional Relationships

To graph a proportional relationship, we need to plot the points on a coordinate plane. The x-axis represents the number of bags of sand ($s$), and the y-axis represents the number of bags of cement ($c$). Since the equation is $c = \frac{1}{3}s$, we can plot the points by multiplying the x-coordinate by $\frac{1}{3}$ to get the y-coordinate.

Analyzing the Graph

When we graph the equation $c = \frac{1}{3}s$, we get a straight line that passes through the origin (0,0). This means that when there are no bags of sand ($s=0$), there are also no bags of cement ($c=0$). As we increase the number of bags of sand ($s$), the number of bags of cement ($c$) also increases proportionally.

Evaluating the Statements

Now that we have a clear understanding of the equation and its graph, let's evaluate the statements.

• Statement A: The proportional relationship is graphed as a straight line that passes through the origin (0,0).
• Statement B: The proportional relationship is graphed as a curve that does not pass through the origin (0,0).

Conclusion

Based on our analysis, we can conclude that the proportional relationship represented by the equation $c = \frac{1}{3}s$ is graphed as a straight line that passes through the origin (0,0). Therefore, Statement A is true.

The Equation of Proportional Relationship: Key Takeaways

• A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other variable.
• The equation $c = \frac{1}{3}s$ represents a proportional relationship between the number of bags of cement ($c$) and the number of bags of sand ($s$).
• The graph of a proportional relationship is a straight line that passes through the origin (0,0).
• The equation $c = \frac{1}{3}s$ is graphed as a straight line that passes through the origin (0,0).

Frequently Asked Questions

Q: What is a proportional relationship?

A: A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other variable.

Q: How do we graph a proportional relationship?

A: To graph a proportional relationship, we need to plot the points on a coordinate plane. The x-axis represents the number of bags of sand ($s$), and the y-axis represents the number of bags of cement ($c$).

Q: What is the graph of a proportional relationship?

A: The graph of a proportional relationship is a straight line that passes through the origin (0,0).

Q: Is the equation $c = \frac{1}{3}s$ graphed as a straight line that passes through the origin (0,0)?

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Introduction

In our previous article, we explored the concept of proportional relationships and analyzed the equation $c = \frac{1}{3}s$. We concluded that the proportional relationship is graphed as a straight line that passes through the origin (0,0). In this article, we will continue to delve into the world of proportional relationships and answer some frequently asked questions.

Q&A Session

Q: What is the difference between a proportional relationship and a non-proportional relationship?

A: A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other variable. A non-proportional relationship, on the other hand, is a relationship between two variables where one variable is not a constant multiple of the other variable.

Q: How do we determine if a relationship is proportional or non-proportional?

A: To determine if a relationship is proportional or non-proportional, we need to check if the ratio of the two variables is constant. If the ratio is constant, then the relationship is proportional. If the ratio is not constant, then the relationship is non-proportional.

Q: What is the equation of a proportional relationship?

A: The equation of a proportional relationship is of the form $y = kx$, where $k$ is a constant.

Q: How do we graph a proportional relationship?

A: To graph a proportional relationship, we need to plot the points on a coordinate plane. The x-axis represents the independent variable, and the y-axis represents the dependent variable.

Q: What is the graph of a proportional relationship?

A: The graph of a proportional relationship is a straight line that passes through the origin (0,0).

Q: Can a proportional relationship have a slope of 0?

A: No, a proportional relationship cannot have a slope of 0. The slope of a proportional relationship is always a non-zero constant.

Q: Can a proportional relationship have a slope of infinity?

A: No, a proportional relationship cannot have a slope of infinity. The slope of a proportional relationship is always a finite non-zero constant.

Q: How do we find the equation of a proportional relationship?

A: To find the equation of a proportional relationship, we need to find the constant of proportionality ($k$) and then use it to write the equation in the form $y = kx$.

Q: What is the constant of proportionality?

A: The constant of proportionality is the constant that multiplies the independent variable to get the dependent variable.

Q: How do we find the constant of proportionality?

A: To find the constant of proportionality, we need to use the given data points and the equation of the proportional relationship to solve for the constant.

Q: Can a proportional relationship have a negative constant of proportionality?

A: Yes, a proportional relationship can have a negative constant of proportionality.

Q: Can a proportional relationship have a positive constant of proportionality?

A: Yes, a proportional relationship can have a positive constant of proportionality.

Q: What is the significance of the constant of proportionality?

A: The constant of proportionality is significant because it tells us the rate at which the dependent variable changes with respect to the independent variable.

Q: How do we use the constant of proportionality in real-world applications?

A: We use the constant of proportionality to make predictions and model real-world phenomena.

Conclusion

In this article, we answered some frequently asked questions about proportional relationships. We hope that this Q&A session has helped to clarify any doubts and provide a better understanding of the concept of proportional relationships.

The Equation of Proportional Relationship: Key Takeaways

• A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other variable.
• The equation of a proportional relationship is of the form $y = kx$, where $k$ is a constant.
• The graph of a proportional relationship is a straight line that passes through the origin (0,0).
• The constant of proportionality is the constant that multiplies the independent variable to get the dependent variable.
• The constant of proportionality is significant because it tells us the rate at which the dependent variable changes with respect to the independent variable.

Frequently Asked Questions

Q: What is the difference between a proportional relationship and a non-proportional relationship?

A: A proportional relationship is a relationship between two variables where one variable is a constant multiple of the other variable. A non-proportional relationship, on the other hand, is a relationship between two variables where one variable is not a constant multiple of the other variable.

Q: How do we determine if a relationship is proportional or non-proportional?

A: To determine if a relationship is proportional or non-proportional, we need to check if the ratio of the two variables is constant. If the ratio is constant, then the relationship is proportional. If the ratio is not constant, then the relationship is non-proportional.

Q: What is the equation of a proportional relationship?

A: The equation of a proportional relationship is of the form $y = kx$, where $k$ is a constant.

Q: How do we graph a proportional relationship?

A: To graph a proportional relationship, we need to plot the points on a coordinate plane. The x-axis represents the independent variable, and the y-axis represents the dependent variable.

Q: What is the graph of a proportional relationship?

A: The graph of a proportional relationship is a straight line that passes through the origin (0,0).

Q: Can a proportional relationship have a slope of 0?

A: No, a proportional relationship cannot have a slope of 0. The slope of a proportional relationship is always a non-zero constant.

Q: Can a proportional relationship have a slope of infinity?

A: No, a proportional relationship cannot have a slope of infinity. The slope of a proportional relationship is always a finite non-zero constant.

Q: How do we find the equation of a proportional relationship?

A: To find the equation of a proportional relationship, we need to find the constant of proportionality ($k$) and then use it to write the equation in the form $y = kx$.

Q: What is the constant of proportionality?

A: The constant of proportionality is the constant that multiplies the independent variable to get the dependent variable.

Q: How do we find the constant of proportionality?

A: To find the constant of proportionality, we need to use the given data points and the equation of the proportional relationship to solve for the constant.

Q: Can a proportional relationship have a negative constant of proportionality?

A: Yes, a proportional relationship can have a negative constant of proportionality.

Q: Can a proportional relationship have a positive constant of proportionality?

A: Yes, a proportional relationship can have a positive constant of proportionality.

Q: What is the significance of the constant of proportionality?

A: The constant of proportionality is significant because it tells us the rate at which the dependent variable changes with respect to the independent variable.

Q: How do we use the constant of proportionality in real-world applications?

A: We use the constant of proportionality to make predictions and model real-world phenomena.