The Equation Y = 5 X Y = 5x Y = 5 X Represents The Amount Of Money That I Earn Washing Dogs In My Neighborhood, Given X X X Is The Number Of Dogs. If I Wash Between 2 And 10 Dogs A Week, What Is The Range Of This Situation?A. $2 \leq X \leq

The Equation of Dog Washing: Understanding the Range of a Linear Situation

The equation $y = 5x$ represents a linear situation where the amount of money earned ($y$) is directly proportional to the number of dogs washed ($x$). In this scenario, we are given that the number of dogs washed per week ranges from 2 to 10. Our goal is to determine the range of this situation, which will provide us with the minimum and maximum amount of money that can be earned within this range.

The equation $y = 5x$ is a linear equation in the slope-intercept form, where $y$ is the dependent variable (the amount of money earned) and $x$ is the independent variable (the number of dogs washed). The slope of the line is 5, indicating that for every additional dog washed, the amount of money earned increases by $5.

To find the range of this situation, we need to determine the minimum and maximum values of $y$ when $x$ ranges from 2 to 10. We can do this by substituting the values of $x$ into the equation and solving for $y$.

Minimum Value of $y$

When $x = 2$, we can substitute this value into the equation to find the minimum value of $y$.

$$y = 5(2)$$

$$y = 10$$

So, the minimum value of $y$ is $10$ when $x = 2$.

Maximum Value of $y$

When $x = 10$, we can substitute this value into the equation to find the maximum value of $y$.

$$y = 5(10)$$

$$y = 50$$

So, the maximum value of $y$ is $50$ when $x = 10$.

Range of the Situation

The range of this situation is the set of all possible values of $y$ when $x$ ranges from 2 to 10. Based on our calculations, the minimum value of $y$ is $10$ and the maximum value of $y$ is $50$. Therefore, the range of this situation is:

$$10 \leq y \leq 50$$

In conclusion, the equation $y = 5x$ represents a linear situation where the amount of money earned is directly proportional to the number of dogs washed. By substituting the values of $x$ into the equation, we can determine the minimum and maximum values of $y$ when $x$ ranges from 2 to 10. The range of this situation is $10 \leq y \leq 50$, indicating that the minimum amount of money that can be earned is $10$ and the maximum amount of money that can be earned is $50$.

• What are some real-world applications of linear equations?
• How can we use linear equations to model real-world situations?
• What are some common mistakes to avoid when working with linear equations?

• Linear equations can be used to model a wide range of real-world situations, including population growth, cost-benefit analysis, and supply and demand.
• To use linear equations to model real-world situations, we need to identify the variables and constants involved, and then use the equation to make predictions or solve problems.
• Some common mistakes to avoid when working with linear equations include:
  • Failing to check the units of the variables and constants involved.
  • Failing to check the domain and range of the equation.
  • Failing to check for extraneous solutions.

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations
  The Equation of Dog Washing: Q&A

In our previous article, we explored the equation $y = 5x$ and how it represents the amount of money earned washing dogs in a neighborhood. We determined the range of this situation, which is $10 \leq y \leq 50$. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the equation $y = 5x$ representing?

A: The equation $y = 5x$ represents the amount of money earned washing dogs in a neighborhood, where $x$ is the number of dogs washed.

Q: What is the slope of the line represented by the equation $y = 5x$?

A: The slope of the line represented by the equation $y = 5x$ is 5, indicating that for every additional dog washed, the amount of money earned increases by $5.

Q: What is the minimum value of $y$ when $x$ ranges from 2 to 10?

A: The minimum value of $y$ is $10$ when $x = 2$.

Q: What is the maximum value of $y$ when $x$ ranges from 2 to 10?

A: The maximum value of $y$ is $50$ when $x = 10$.

Q: What is the range of this situation?

A: The range of this situation is $10 \leq y \leq 50$.

Q: How can we use linear equations to model real-world situations?

A: We can use linear equations to model real-world situations by identifying the variables and constants involved, and then using the equation to make predictions or solve problems.

Q: What are some common mistakes to avoid when working with linear equations?

A: Some common mistakes to avoid when working with linear equations include:

• Failing to check the units of the variables and constants involved.
• Failing to check the domain and range of the equation.
• Failing to check for extraneous solutions.

Q: What are some real-world applications of linear equations?

A: Linear equations have many real-world applications, including:

• Population growth
• Cost-benefit analysis
• Supply and demand
• Finance
• Science

Q: How can we use linear equations to solve problems in real-world situations?

A: We can use linear equations to solve problems in real-world situations by:

• Identifying the variables and constants involved
• Using the equation to make predictions or solve problems
• Checking the units of the variables and constants involved
• Checking the domain and range of the equation
• Checking for extraneous solutions

In conclusion, the equation $y = 5x$ represents a linear situation where the amount of money earned is directly proportional to the number of dogs washed. By answering some frequently asked questions related to this topic, we have gained a deeper understanding of how linear equations can be used to model real-world situations.

• What are some other real-world applications of linear equations?
• How can we use linear equations to solve problems in real-world situations?
• What are some common mistakes to avoid when working with linear equations?

• Some other real-world applications of linear equations include:
  • Physics
  • Engineering
  • Computer Science
• We can use linear equations to solve problems in real-world situations by identifying the variables and constants involved, and then using the equation to make predictions or solve problems.
• Some common mistakes to avoid when working with linear equations include:
  • Failing to check the units of the variables and constants involved.
  • Failing to check the domain and range of the equation.
  • Failing to check for extraneous solutions.

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations