Select The Correct Answer.Esther Works For A Marketing Company. She Earns $\$12$ Per Hour, And She Gets A $\$50$ Travel Allowance Every Month. Which Linear Equation Could Be Used To Find Her Monthly Pay Rate?A. $y = 50x +

As a marketing professional, Esther's income is comprised of her hourly wage and a monthly travel allowance. To determine her monthly pay rate, we need to create a linear equation that takes into account both of these components.

The Importance of Linear Equations in Real-World Scenarios

Linear equations are a fundamental concept in mathematics that have numerous applications in real-world scenarios. In this case, we can use a linear equation to model Esther's monthly pay rate, which is a combination of her hourly wage and the monthly travel allowance.

Breaking Down Esther's Income Components

Esther earns $\$12$ per hour, which means that her hourly wage is a fixed value. Additionally, she receives a $\$50$ travel allowance every month, which is a constant value. To create a linear equation that represents her monthly pay rate, we need to consider both of these components.

Creating a Linear Equation for Esther's Monthly Pay Rate

A linear equation is typically represented in the form of $y = mx + b$, where $y$ is the dependent variable, $x$ is the independent variable, $m$ is the slope, and $b$ is the y-intercept. In this case, we can use the following linear equation to represent Esther's monthly pay rate:

$$y = 12x + 50$$

Here, $y$ represents Esther's monthly pay rate, $x$ represents the number of hours she works, and $12x$ represents her hourly wage. The constant term $50$ represents the monthly travel allowance.

Interpreting the Linear Equation

The linear equation $y = 12x + 50$ can be interpreted as follows:

• When $x = 0$, $y = 50$, which means that Esther's monthly pay rate is $\$50$ when she works zero hours.
• When $x = 1$, $y = 62$, which means that Esther's monthly pay rate is $\$62$ when she works one hour.
• When $x = 2$, $y = 74$, which means that Esther's monthly pay rate is $\$74$ when she works two hours.

Conclusion

In conclusion, the linear equation $y = 12x + 50$ can be used to find Esther's monthly pay rate. This equation takes into account both her hourly wage and the monthly travel allowance, providing a comprehensive model of her income. By using this equation, we can determine Esther's monthly pay rate for any given number of hours worked.

Discussion

Now that we have created a linear equation to represent Esther's monthly pay rate, let's discuss some of the implications of this equation.

• Hourly Wage: The hourly wage of $\$12$ is a fixed value that represents Esther's earnings per hour. This value can be adjusted to reflect changes in her hourly wage.
• Monthly Travel Allowance: The monthly travel allowance of $\$50$ is a constant value that represents Esther's fixed expenses. This value can be adjusted to reflect changes in her travel expenses.
• Monthly Pay Rate: The monthly pay rate is a dependent variable that represents Esther's total earnings for a given month. This value can be calculated using the linear equation $y = 12x + 50$.

Example Questions

Here are some example questions that can be used to test your understanding of the linear equation $y = 12x + 50$.

• What is Esther's monthly pay rate when she works 3 hours?
• What is Esther's monthly pay rate when she works 5 hours?
• What is the value of the constant term $50$ in the linear equation $y = 12x + 50$?

Answer Key

Here are the answers to the example questions.

• When $x = 3$, $y = 50 + 12(3) = 86$, which means that Esther's monthly pay rate is $\$86$ when she works 3 hours.
• When $x = 5$, $y = 50 + 12(5) = 110$, which means that Esther's monthly pay rate is $\$110$ when she works 5 hours.
• The value of the constant term $50$ in the linear equation $y = 12x + 50$ represents the monthly travel allowance.
  Q&A: Understanding Esther's Monthly Pay Rate =====================================================

In our previous article, we created a linear equation to represent Esther's monthly pay rate. Now, let's answer some frequently asked questions about this equation.

Q: What is the purpose of the linear equation $y = 12x + 50$?

A: The purpose of the linear equation $y = 12x + 50$ is to represent Esther's monthly pay rate, which is a combination of her hourly wage and the monthly travel allowance.

Q: What is the meaning of the constant term $50$ in the linear equation $y = 12x + 50$?

A: The constant term $50$ in the linear equation $y = 12x + 50$ represents the monthly travel allowance that Esther receives.

Q: What is the meaning of the slope $12$ in the linear equation $y = 12x + 50$?

A: The slope $12$ in the linear equation $y = 12x + 50$ represents Esther's hourly wage. For every hour she works, her pay rate increases by $\$12$.

Q: How can I use the linear equation $y = 12x + 50$ to find Esther's monthly pay rate?

A: To find Esther's monthly pay rate using the linear equation $y = 12x + 50$, simply plug in the number of hours she works into the equation. For example, if Esther works 3 hours, her monthly pay rate would be $y = 12(3) + 50 = 86$.

Q: What is the y-intercept of the linear equation $y = 12x + 50$?

A: The y-intercept of the linear equation $y = 12x + 50$ is $50$, which represents Esther's monthly pay rate when she works zero hours.

Q: How can I adjust the linear equation $y = 12x + 50$ to reflect changes in Esther's hourly wage or monthly travel allowance?

A: To adjust the linear equation $y = 12x + 50$ to reflect changes in Esther's hourly wage or monthly travel allowance, simply update the slope and constant term accordingly. For example, if Esther's hourly wage increases to $\$15$, the new linear equation would be $y = 15x + 50$.

Q: Can I use the linear equation $y = 12x + 50$ to compare Esther's monthly pay rate to other employees?

A: Yes, you can use the linear equation $y = 12x + 50$ to compare Esther's monthly pay rate to other employees. Simply plug in the number of hours worked by each employee into the equation and compare the resulting monthly pay rates.

Q: What are some real-world applications of the linear equation $y = 12x + 50$?

A: Some real-world applications of the linear equation $y = 12x + 50$ include:

• Modeling employee salaries and benefits
• Calculating hourly wages and overtime pay
• Creating budgets and financial plans
• Analyzing data and making informed decisions

Conclusion

In conclusion, the linear equation $y = 12x + 50$ is a powerful tool for modeling Esther's monthly pay rate. By understanding the components of this equation, you can use it to make informed decisions and analyze data in a variety of real-world scenarios.