Select The Correct Answer.Esther Works For A Marketing Company. She Earns $12 Per Hour And Receives A $50 Travel Allowance Every Month. Which Linear Equation Could Be Used To Find Her Monthly Pay Rate?A. { Y = 50x + 12 $}$B.
Introduction
In the world of mathematics, linear equations are used to model various real-life scenarios. These equations help us understand the relationship between different variables and make predictions based on that relationship. In this article, we will explore how linear equations can be used to find the monthly pay rate of Esther, a marketing professional.
Esther's Monthly Pay Rate
Esther works for a marketing company and earns $12 per hour. She also receives a $50 travel allowance every month. To find her monthly pay rate, we need to consider both her hourly wage and the travel allowance. Let's break down the problem step by step.
Step 1: Define the Variables
- x: The number of hours Esther works in a month.
- y: Esther's monthly pay rate.
Step 2: Identify the Constants
- $12: Esther's hourly wage.
- $50: The travel allowance she receives every month.
Step 3: Write the Linear Equation
A linear equation is a mathematical expression that represents a linear relationship between two variables. In this case, we want to find the monthly pay rate (y) based on the number of hours Esther works (x). We can write the linear equation as:
y = 12x + 50
Why This Equation?
This equation represents the relationship between Esther's hourly wage and the travel allowance. The term 12x represents Esther's earnings based on her hourly wage, while the constant term 50 represents the travel allowance she receives every month.
Comparing the Options
Let's compare the equation we derived with the options provided:
A. y = 50x + 12 B. y = 12x + 50
Option A
y = 50x + 12
This equation is incorrect because it swaps the hourly wage and the travel allowance. The correct equation should have the hourly wage (12) multiplied by the number of hours (x), and the travel allowance (50) as a constant term.
Option B
y = 12x + 50
This equation is correct because it accurately represents the relationship between Esther's hourly wage and the travel allowance.
Conclusion
In conclusion, the correct linear equation to find Esther's monthly pay rate is y = 12x + 50. This equation takes into account both her hourly wage and the travel allowance she receives every month. By using this equation, we can calculate Esther's monthly pay rate based on the number of hours she works.
Real-Life Applications
Linear equations like this one have numerous real-life applications. They can be used to model various scenarios, such as:
- Business: To calculate employee salaries, bonuses, or commissions.
- Finance: To determine interest rates, investment returns, or loan payments.
- Science: To model population growth, chemical reactions, or physical phenomena.
Tips and Tricks
When working with linear equations, remember to:
- Identify the variables: Clearly define the variables and their relationships.
- Identify the constants: Clearly define the constants and their values.
- Write the equation: Use the variables and constants to write the linear equation.
By following these tips and tricks, you can effectively use linear equations to solve real-life problems and make informed decisions.
Final Thoughts
Introduction
In our previous article, we explored how to use linear equations to find Esther's monthly pay rate. Linear equations are a fundamental concept in mathematics, and they have numerous real-life applications. In this article, we will answer some frequently asked questions (FAQs) about linear equations.
Q: What is a linear equation?
A linear equation is a mathematical expression that represents a linear relationship between two variables. It is an equation in which the highest power of the variable(s) is 1.
Q: What are the characteristics of a linear equation?
A linear equation has the following characteristics:
- Linear relationship: The equation represents a linear relationship between the variables.
- Highest power of 1: The highest power of the variable(s) is 1.
- Constant term: The equation has a constant term.
Q: How do I write a linear equation?
To write a linear equation, you need to:
- Identify the variables: Clearly define the variables and their relationships.
- Identify the constants: Clearly define the constants and their values.
- Write the equation: Use the variables and constants to write the linear equation.
Q: What is the slope-intercept form of a linear equation?
The slope-intercept form of a linear equation is:
y = mx + b
where:
- m: The slope of the line.
- x: The independent variable.
- b: The y-intercept.
Q: What is the standard form of a linear equation?
The standard form of a linear equation is:
ax + by = c
where:
- a: The coefficient of x.
- b: The coefficient of y.
- c: The constant term.
Q: How do I solve a linear equation?
To solve a linear equation, you need to:
- Isolate the variable: Isolate the variable on one side of the equation.
- Simplify the equation: Simplify the equation by combining like terms.
- Check the solution: Check the solution to ensure it is correct.
Q: What are some real-life applications of linear equations?
Linear equations have numerous real-life applications, including:
- Business: To calculate employee salaries, bonuses, or commissions.
- Finance: To determine interest rates, investment returns, or loan payments.
- Science: To model population growth, chemical reactions, or physical phenomena.
Q: What are some common mistakes to avoid when working with linear equations?
Some common mistakes to avoid when working with linear equations include:
- Incorrectly identifying the variables: Failing to clearly define the variables and their relationships.
- Incorrectly identifying the constants: Failing to clearly define the constants and their values.
- Not simplifying the equation: Failing to simplify the equation by combining like terms.
Conclusion
Linear equations are a fundamental concept in mathematics, and they have numerous real-life applications. By understanding how to write and use linear equations, you can make predictions, calculate values, and make informed decisions. In this article, we answered some frequently asked questions (FAQs) about linear equations. We hope this article has helped you understand the importance of linear equations in real-life scenarios.
Additional Resources
For more information on linear equations, we recommend the following resources:
- Textbooks: "Linear Algebra and Its Applications" by Gilbert Strang and "Linear Equations and Inequalities" by Michael Sullivan.
- Online tutorials: Khan Academy's Linear Equations tutorial and Mathway's Linear Equations tutorial.
- Practice problems: IXL's Linear Equations practice problems and Math Open Reference's Linear Equations practice problems.
Final Thoughts
Linear equations are a powerful tool for modeling real-life scenarios. By understanding how to write and use these equations, you can make predictions, calculate values, and make informed decisions. We hope this article has helped you understand the importance of linear equations in real-life scenarios.