Sophia Walked A Total Of 6 Miles In Two Days. On The First Day, She Walked 2 Miles. The Equation $m + 2 = 6$ Can Be Used To Find The Number Of Miles $m$ She Walked On The Second Day.Which Model Shows The Equation?A. $\square
Introduction
In this article, we will delve into a mathematical problem that involves solving an equation to find the number of miles Sophia walked on the second day. The problem is presented as follows: Sophia walked a total of 6 miles in two days. On the first day, she walked 2 miles. The equation $m + 2 = 6$ can be used to find the number of miles $m$ she walked on the second day. Our goal is to identify the model that represents this equation.
The Equation: A Closer Look
The given equation is $m + 2 = 6$. This is a linear equation in one variable, where $m$ represents the number of miles Sophia walked on the second day. To solve for $m$, we need to isolate the variable on one side of the equation.
Solving the Equation
To solve the equation, we can subtract 2 from both sides of the equation. This will give us:
Simplifying the equation, we get:
This means that Sophia walked 4 miles on the second day.
Identifying the Model
Now that we have solved the equation, we need to identify the model that represents this equation. The equation $m + 2 = 6$ can be represented as a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
The Linear Equation Model
A linear equation in the form of $y = mx + b$ can be represented graphically as a straight line. The slope of the line represents the rate of change of the variable, while the y-intercept represents the value of the variable when the other variable is equal to zero.
The Slope-Intercept Form
The slope-intercept form of a linear equation is given by:
In this form, $m$ represents the slope of the line, and $b$ represents the y-intercept.
The Equation in Slope-Intercept Form
To convert the equation $m + 2 = 6$ to slope-intercept form, we can subtract 2 from both sides of the equation. This gives us:
Substituting this value into the equation, we get:
This is the slope-intercept form of the equation.
Conclusion
In conclusion, the equation $m + 2 = 6$ can be represented as a linear equation in the form of $y = mx + b$. The slope of the line represents the rate of change of the variable, while the y-intercept represents the value of the variable when the other variable is equal to zero. By solving the equation, we found that Sophia walked 4 miles on the second day.
The Final Answer
The final answer is that the equation $m + 2 = 6$ can be represented as a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The slope of the line represents the rate of change of the variable, while the y-intercept represents the value of the variable when the other variable is equal to zero.
The Model
The model that represents the equation is a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
The Graph
The graph of the equation is a straight line with a slope of 4 and a y-intercept of 2.
The Solution
The solution to the equation is $m = 4$, which means that Sophia walked 4 miles on the second day.
The Equation in Slope-Intercept Form
The equation in slope-intercept form is $y = 4x + 2$.
The Final Answer
Introduction
In our previous article, we explored a mathematical problem that involved solving an equation to find the number of miles Sophia walked on the second day. We also identified the model that represents this equation. In this article, we will answer some frequently asked questions (FAQs) related to the problem and the model.
Q: What is the equation that represents the problem?
A: The equation that represents the problem is $m + 2 = 6$, where $m$ is the number of miles Sophia walked on the second day.
Q: How do I solve the equation?
A: To solve the equation, you can subtract 2 from both sides of the equation. This will give you:
Simplifying the equation, you get:
This means that Sophia walked 4 miles on the second day.
Q: What is the model that represents the equation?
A: The model that represents the equation is a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Q: What is the slope of the line?
A: The slope of the line represents the rate of change of the variable. In this case, the slope is 4, which means that for every 1 unit increase in the variable, the value of the variable increases by 4 units.
Q: What is the y-intercept of the line?
A: The y-intercept of the line represents the value of the variable when the other variable is equal to zero. In this case, the y-intercept is 2, which means that when the other variable is equal to zero, the value of the variable is 2.
Q: How do I graph the equation?
A: To graph the equation, you can use the slope-intercept form of the equation, which is $y = mx + b$. You can plot the y-intercept on the y-axis and then use the slope to find the other points on the line.
Q: What is the solution to the equation?
A: The solution to the equation is $m = 4$, which means that Sophia walked 4 miles on the second day.
Q: Can I use this model to solve other problems?
A: Yes, you can use this model to solve other problems that involve linear equations. The model can be applied to a wide range of problems, including those that involve rates of change, slopes, and y-intercepts.
Q: How do I apply the model to real-world problems?
A: To apply the model to real-world problems, you can use the same steps that we used to solve the equation. You can identify the variables, set up the equation, solve for the variable, and then use the model to make predictions or draw conclusions.
Conclusion
In conclusion, the model that represents the equation $m + 2 = 6$ is a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We have answered some frequently asked questions related to the problem and the model, and we have provided some tips on how to apply the model to real-world problems.
Frequently Asked Questions
- Q: What is the equation that represents the problem?
- A: The equation that represents the problem is $m + 2 = 6$, where $m$ is the number of miles Sophia walked on the second day.
- Q: How do I solve the equation?
- A: To solve the equation, you can subtract 2 from both sides of the equation.
- Q: What is the model that represents the equation?
- A: The model that represents the equation is a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
- Q: What is the slope of the line?
- A: The slope of the line represents the rate of change of the variable.
- Q: What is the y-intercept of the line?
- A: The y-intercept of the line represents the value of the variable when the other variable is equal to zero.
- Q: How do I graph the equation?
- A: To graph the equation, you can use the slope-intercept form of the equation.
- Q: What is the solution to the equation?
- A: The solution to the equation is $m = 4$, which means that Sophia walked 4 miles on the second day.
- Q: Can I use this model to solve other problems?
- A: Yes, you can use this model to solve other problems that involve linear equations.
- Q: How do I apply the model to real-world problems?
- A: To apply the model to real-world problems, you can use the same steps that we used to solve the equation.